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Factorising method

Recognise two squares

x² - 9
x2 - 9x2-32A2 - B2 = (A - B)(A + B)(x - 3)(x + 3)

A difference of squares has one square minus another square.

Detailed notes

Worked Example

Factor x² - 9 by recognising it as one square minus another square.

Step 1: Recognise the pattern

A difference of squares has the form A² - B².

A2 - B2 = (A + B)(A - B)

Step 2: Rewrite both parts as squares

The first square is x². The number 9 is 3².

x2 - 9 = x2 - 32

Step 3: Identify A and B

Here, A is x and B is 3.

A = x
B = 3

Step 4: Use opposite signs

The factors use the same two terms, one with plus and one with minus.

x2 - 9 = (x + 3)(x - 3)