# How do you determine whether 25x^2-60x+36 is a perfect square trinomial?

Aug 17, 2017

Can the trinomial be factored into two identical binomials.

#### Explanation:

The answer is yes it can

$25 {x}^{2} - 60 x + 36 = \left(5 x - 6\right) \times \left(5 x - 6\right)$ so

$25 {x}^{2} = 60 x + 36 = {\left(5 x - 6\right)}^{2}$

Aug 17, 2017

Look for the clues as described below.

#### Explanation:

If the trinomial is a perfect square trinomial, there will be some properties to check for.

$a {x}^{2} \pm b x + c$

• both $a \mathmr{and} c$ must be perfect squares, with plus signs
• check whether $b = 2 \times \sqrt{a} \times \sqrt{c}$

In this case: $a = 25 = {5}^{2} \text{ } \mathmr{and} c = 36 = {6}^{2}$

$2 \times \sqrt{25} \times \sqrt{36} = 2 \times 5 \times 6 \times = 60$
$b = 60$

Therefore we know that $25 {x}^{2} - 60 x + 25$ is the square of a binomial.

It will factorise as:

$25 {x}^{2} - 60 x + 25 = {\left(5 x - 6\right)}^{2}$