Recall that

Therefore, if a trinomial is of the form ( *x*) ^{2} + 2( *x*)( *y*) + ( *y*) ^{2}, it can be factored into the square of a binomial.

##### Example 1

Is 4 *x* ^{2} – 20 *x* + 25 a square trinomial? If so, factor it into the square of some binomial.

4 *x* ^{2} = (2 *x*) ^{2} and 25 = (–5) ^{2} and –20 *x* = 2(2 *x*)(–5)

So it is a square trinomial, which factors as follows.

4 *x* ^{2} – 20 *x* + 25 = (2 *x* – 5) ^{2}

##### Example 2

Is *x* ^{2} + 10 *x* + 9 a square trinomial?

*x* ^{2} = ( *x*) ^{2} and 9 = 3 ^{2} but 10 *x* ≠ 2( *x*)(3)

So it is not a square trinomial. But *x* ^{2} + 10 *x* + 9 is factorable.

*x* ^{2} + 10 *x* + 9 = ( *x* + 1)( *x* + 9)