Square Trinomials

Recall that

equation

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)