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Expanding-Double-Brackets Wjec-Eduqas Foundation
Exam code:C300
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
-
-
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
-
-
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
-
-
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
-
-
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
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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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