Question

Determine whether the polynomial is a difference of squares and if it is, factor it.

y2 – 225



is a difference of squares: (y – 15)(y + 15)

is not a difference of squares

is a difference of squares: (y + 15)2

is a difference of squares: (y – 15)2

Answer 1

Remember these three formulas (really, learn these by heart):


`{(a + b)}^(2) = a^(2) + 2ab + b^(2)`


`{(a - b)}^(2) = a^(2) - 2ab + b^(2)`


`(a + b)(a - b) = a^(2) - b^(2)`

The stated formula is a manifestation of the last of these three. So indeed,


`(y + 15)(y - 15) = y^(2) - 225`