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 a difference of squares: (y – 15)2

is not a difference of squares

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

Answer 1

The correct answer option is: it is a difference of squares: (y – 15)(y + 15)

Explanation:

We are given a polynomial and we are to determine if it is a difference of squares.

Let us recall the algebraic formulas which include:

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

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

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

So if we look closely, we can conclude that the given polynomial observes the third formula of the perfect squares.

Hence, we can say that it is a difference of squares: (y – 15)(y + 15)

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