Expanding the expression `(a + 3)(a - 3)` gives an answer of `a^2 - 9`: there is no `a` term.
`a^2 - 9` can be written as `a^2 - 3^2`: both terms are squared and the subtraction gives the difference.
Note that the constant in the expanded expression is a negative.
This is known as the difference of two squares.
Factorise `b^2 - 81`
No `b` term and √81 = 9 and -9, so is the difference of two squares.
Answer: `(b + 9)(b - 9)`
Show `a^2x^2 - y^2` as the difference of two squares.
First term: `sqrt(a^2x^2) = ax`
Second term: `sqrt(y^2) = +y text( and ) -y`
`a^2x^2 - y^2 = (ax + y)(ax - y)`
Answer: `(ax + y)(ax - y)`