# For what value of n is x^2-10x+n a perfect square trinomial?

Jun 12, 2015

$n = {5}^{2} = 25$ since every perfect square trinomial is of the form ${a}^{2} + 2 a b + {b}^{2}$

#### Explanation:

Every perfect square trinomial is of the form:

${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$

In the given example, $a = x$ and $2 a b = 2 x \cdot b = - 10 x$,

so $b = \frac{- 10 x}{2 x} = - 5$ and $n = {b}^{2} = {\left(- 5\right)}^{2} = {5}^{2} = 25$.