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Year 9AC9M9A02
Summary of important concepts

Factorising — Difference of Two Squares

Simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions.

Two perfect squares separated by a minus sign. Never a plus.

Worked example

e.g. x2−1x^{2} - 1
  1. Identify perfect squares separated by a minusx2−1x^{2} - 1
  2. Write two brackets, a different sign in each(   +   )(   −   )(\ \ \ + \ \ \ )(\ \ \ - \ \ \ )
  3. Put the square root of each term into both brackets(x+1)(x−1)(x+1)(x-1)
  4. Simplify if possible(x+1)(x−1)(x+1)(x-1)

Practice

1
x2−25x^{2} - 25
Answer(x+5)(x−5)(x+5)(x-5)
2
9x2−169x^{2} - 16
Answer(3x+4)(3x−4)(3x+4)(3x-4)
3
49−y249 - y^{2}
Answer(7+y)(7−y)(7+y)(7-y)
4
4x2−81y24x^{2} - 81y^{2}
Answer(2x+9y)(2x−9y)(2x+9y)(2x-9y)
5
(x+2)2−x2(x+2)^{2} - x^{2}
Answer(2x+2)(2)=4x+4(2x+2)(2) = 4x+4
6
x4−16x^{4} - 16
Answer(x2+4)(x+2)(x−2)(x^{2}+4)(x+2)(x-2)
7
50x2−250x^{2} - 2
Answer2(5x+1)(5x−1)2(5x+1)(5x-1)
8
(3x−1)2−9(3x-1)^{2} - 9
Answer(3x+2)(3x−4)(3x+2)(3x-4)
Next step
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