GCSE(F) GCSE(H)

Expanding the expression (*a* + 3)(*a* - 3) gives an answer of *a*^{2} - 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**.

1. Factorise *b*^{2} - 81.

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

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

2. Factorise *x*^{2} - *y*

Answer: (*x* + √*y*)(*x* - √*y*)

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

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