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

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

Step 1

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

${(2 x)}^{2} + 28 x y + 49 y^{2}$

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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