Factor 49x^2-14xy+y^2

$49 x^{2} - 14 x y + y^{2}$

Step 1

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

${(7 x)}^{2} - 14 x y + y^{2}$

Step 2

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

$14 x y = 2 \cdot (7 x) \cdot y$

Step 3

Rewrite the polynomial.

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

Step 4

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

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