Factor by Grouping 25+70x+49x^2

$25 + 70 x + 49 x^{2}$

Step 1

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

$5^{2} + 70 x + 49 x^{2}$

Step 2

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

$5^{2} + 70 x + {(7 x)}^{2}$

Step 3

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

$70 x = 2 \cdot 5 \cdot (7 x)$

Step 4

Rewrite the polynomial.

$5^{2} + 2 \cdot 5 \cdot (7 x) + {(7 x)}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5$ and $b = 7 x$ .

${(5 + 7 x)}^{2}$