Factor 49x^2+28xy+4y^2

$49 x^{2} + 28 x y + 4 y^{2}$

Step 1

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

${(7 x)}^{2} + 28 x y + 4 y^{2}$

Step 2

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

${(7 x)}^{2} + 28 x y + {(2 y)}^{2}$

Step 3

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

$28 x y = 2 \cdot (7 x) \cdot (2 y)$

Step 4

Rewrite the polynomial.

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

Step 5

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

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