Factor 49y^2-28y+4

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

Step 1

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

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

Step 2

Rewrite $4$ as $2^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

${(7 y - 2)}^{2}$