Maths Gcse Aqa Foundation
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Scatter-Graphs-And-Correlation Aqa Foundation2 主题
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Statistical-Diagrams Aqa Foundation6 主题
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Averages-Ranges-And-Data Aqa Foundation7 主题
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Tree-Diagrams-And-Combined-Probability Aqa Foundation2 主题
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Simple-Probability-Diagrams Aqa Foundation4 主题
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Transformations Aqa Foundation4 主题
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Vectors Aqa Foundation3 主题
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Pythagoras-And-Trigonometry Aqa Foundation5 主题
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Congruence-Similarity-And-Geometrical-Proof Aqa Foundation5 主题
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Volume-And-Surface-Area Aqa Foundation3 主题
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Circles-Arcs-And-Sectors Aqa Foundation3 主题
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Area-And-Perimeter Aqa Foundation4 主题
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Bearings-Scale-Drawing-Constructions-And-Loci Aqa Foundation5 主题
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2D-And-3D-Shapes Aqa Foundation4 主题
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Angles-In-Polygons-And-Parallel-Lines Aqa Foundation5 主题
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Symmetry-And-Shapes Aqa Foundation4 主题
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Exchange-Rates-And-Best-Buys Aqa Foundation2 主题
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Standard-And-Compound-Units Aqa Foundation5 主题
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Direct-And-Inverse-Proportion Aqa Foundation1 主题
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Ratio-Problem-Solving Aqa Foundation2 主题
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Sequences Aqa Foundation4 主题
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Solving-Inequalities Aqa Foundation3 主题
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Real-Life-Graphs Aqa Foundation4 主题
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Graphs-Of-Functions Aqa Foundation3 主题
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Linear-Graphs Aqa Foundation3 主题
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Coordinate-Geometry Aqa Foundation3 主题
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Functions Aqa Foundation1 主题
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Forming-And-Solving-Equations Aqa Foundation2 主题
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Simultaneous-Equations Aqa Foundation1 主题
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Solving-Quadratic-Equations Aqa Foundation1 主题
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Linear-Equations Aqa Foundation3 主题
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Algebraic-Reasoning Aqa Foundation1 主题
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Rearranging-Formulas Aqa Foundation1 主题
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Introduction Aqa Foundation10 主题
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Relative-And-Expected-Frequency Aqa Foundation
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Sample-Space-Diagrams Aqa Foundation
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Basic-Probability Aqa Foundation
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Sharing-In-A-Ratio Aqa Foundation
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Equivalent-And-Simplified-Ratios Aqa Foundation
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Introduction-To-Ratios Aqa Foundation
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Collecting-Like-Terms Aqa Foundation
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Substitution Aqa Foundation
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Algebraic-Vocabulary Aqa Foundation
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Algebraic-Notation Aqa Foundation
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Relative-And-Expected-Frequency Aqa Foundation
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Factorising Aqa Foundation3 主题
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Expanding-Brackets Aqa Foundation2 主题
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Algebraic-Roots-And-Indices Aqa Foundation1 主题
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Using-A-Calculator Aqa Foundation1 主题
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Exact-Values Aqa Foundation1 主题
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Rounding-Estimation-And-Error-Intervals Aqa Foundation4 主题
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Fractions-Decimals-And-Percentages Aqa Foundation2 主题
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Simple-And-Compound-Interest-Growth-And-Decay Aqa Foundation4 主题
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Percentages Aqa Foundation5 主题
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Fractions Aqa Foundation6 主题
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Powers-Roots-And-Standard-Form Aqa Foundation4 主题
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Types-Of-Number-Prime-Factors-Hcf-And-Lcm Aqa Foundation6 主题
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Number-Operations Aqa Foundation9 主题
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Counting-Principles Aqa Foundation
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Related-Calculations Aqa Foundation
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Multiplication-And-Division Aqa Foundation
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Addition-And-Subtraction Aqa Foundation
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Money-Calculations Aqa Foundation
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Negative-Numbers Aqa Foundation
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Place-Value Aqa Foundation
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Order-Of-Operations-Bidmasbodmas Aqa Foundation
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Mathematical-Operations Aqa Foundation
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Counting-Principles Aqa Foundation
Expanding-Double-Brackets Aqa Foundation
Exam code:8300
Expanding two brackets
How do I expand two brackets using FOIL?
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Every term in the first bracket must be multiplied by every term in the second bracket
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Expanding (x + 1)(x + 3) requires 4 multiplications in total
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A good way to remember all the multiplications is FOIL
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F = First: multiply together the first terms in each bracket
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O = Outside: multiply the first term in the first bracket by the last term in the last bracket
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Visually, these are the outer terms
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I = Inside: multiply the last term in the first bracket by the first term in the last bracket
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Visually, these are the inner terms
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L = Last: multiply together the last terms in each bracket
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It helps to put negative terms in brackets when multiplying
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Simplify the final answer by collecting like terms (if there are any)
How do I expand two brackets using a grid?
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You may prefer a more visual method using a grid
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To expand (x + 1)(x + 3), write out the brackets as row and column headings of a grid
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They can be in either direction
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Remember to write the appropriate sign in front of each term
x
+1
x
+3
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For each cell in the grid, multiply the term in the row heading by the term in the column heading
x
+1
x
x2
x
+3
3x
3
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Add together all the terms inside the grid to get the answer
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x2 + x + 3x + 3
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Collect like terms
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x2 + 4x + 3
How do I expand a bracket squared?
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Remember that a square number is a number multiplied by itself
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Write (x + 3)2 as (x + 3)(x + 3) and use one of the methods above
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With FOIL: (x + 3)(x + 3) = x2 + 3x + 3x + 9
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Then collect like terms: x2 + 6x + 9
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Do not make the common mistake of saying (x + 3)2 is x2 + 32
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This cannot be true, try substituting in x = 1
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you would get (1 + 3)2 = 42 = 16 on the left
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but 12 + 32 = 1 + 9 = 10 on the right
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Worked Example
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.
Using FOIL, multiply together the first, outer, inner and last terms
<img alt=”space space space space space space space straight F space space space space space space space space space space space space space space space space space space straight O space space space space space space space space space space space space space space space space space space space space space straight I space space space space space space space space space space space space space space space space space space space space space space space straight L
circle enclose 2 x cross times x end enclose plus circle enclose 2 x cross times 4 end enclose plus circle enclose open parentheses negative 3 close parentheses cross times x end enclose plus circle enclose open parentheses negative 3 close parentheses cross times 4 end enclose” data-mathml='<math ><semantics><mrow><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mi mathvariant=”normal” >F</mi><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mi mathvariant=”normal” >O</mi><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mi mathvariant=”normal” >I</mi><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mo > </mo><mi mathvariant=”normal” >L</mi><mspace linebreak=”newline”></mspace><menclose notation=”circle”><mn>2</mn><mi>x</mi><mo>×</mo><mi>x</mi></menclose><mo >+</mo><menclose notation=”circle”><mn>2</mn><mi>x</mi><mo>×</mo><mn>4</mn></menclose><mo >+</mo><menclose notation=”circle”><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>×</mo><mi>x</mi></menclose><mo >+</mo><menclose notation=”circle”><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>×</mo><mn>4</mn></menclose></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”working” height=”58″ role=”math” 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