Factor t^2+10t+25

$t^{2} + 10 t + 25$

Step 1

Rewrite $25$ as $5^{2}$ .

$t^{2} + 10 t + 5^{2}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$10 t = 2 \cdot t \cdot 5$

Step 3

Rewrite the polynomial.

$t^{2} + 2 \cdot t \cdot 5 + 5^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = t$ and $b = 5$ .

${(t + 5)}^{2}$