Question

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

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,

$(y + 15)(y - 15) = y^{2} - 225$