Difference-Of-Two-Squares Aqa Higher

Difference of two squares

What is the difference of two squares?

• When a “squared” quantity is subtracted from another “squared” quantity, you get the difference of two squares

  • For example:

    • a² – b²

    • 9² – 5²

    • (x + 1)² – (x – 4)²

    • 4m² – 25n², which is (2m)² – (5n)²

How do I factorise the difference of two squares?

• a² – b² factorises to (a + b)(a – b)

  • This can be shown by expanding the brackets

    • 

  • The brackets can swap order

    • a² – b² = (a + b)(a – b) = (a – b)(a + b)

    • (but terms inside a bracket cannot swap order)

• For example,

  • This is the same as <img alt=”open parentheses x minus 3 close parentheses open parentheses x plus 3 close parentheses” data-mathml=”<math ><semantics><mrow><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’