Factor 49c^2+70cd+25d^2

$49 c^{2} + 70 c d + 25 d^{2}$

Step 1

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

${(7 c)}^{2} + 70 c d + 25 d^{2}$

Step 2

Rewrite $25 d^{2}$ as ${(5 d)}^{2}$ .

${(7 c)}^{2} + 70 c d + {(5 d)}^{2}$

Step 3

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

$70 c d = 2 \cdot (7 c) \cdot (5 d)$

Step 4

Rewrite the polynomial.

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

Step 5

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

${(7 c + 5 d)}^{2}$