Difference of Two Squares

Difference of Two Squares

GCSE(F) GCSE(H)

Expanding the expression (a + 3)(a - 3) gives an answer of a2 - 9: there is no a term.

The constants in each bracket are equal and opposite; and are the square roots of the constant in the expanded expression.

This is known as the difference of two squares.

Examples

1. Factorise b2 - 81.

Answer: (b + 9)(b - 9)

No b term, so difference of two squares. The constants are given by √81.

2. Factorise x2 - y

Answer: (x + √y)(x - √y)

No x term, so difference of two squares. The constant term is given by √y.