Factor 10xy+0.25x^2+100y^2

$10 x y + 0.25 x^{2} + 100 y^{2}$

Step 1

Factor $0.25$ out of $10 x y + 0.25 x^{2} + 100 y^{2}$ .

Factor $0.25$ out of $10 x y$ .

$0.25 (40 x y) + 0.25 x^{2} + 100 y^{2}$

Factor $0.25$ out of $0.25 x^{2}$ .

$0.25 (40 x y) + 0.25 (x^{2}) + 100 y^{2}$

Factor $0.25$ out of $100 y^{2}$ .

$0.25 (40 x y) + 0.25 (x^{2}) + 0.25 (400 y^{2})$

Factor $0.25$ out of $0.25 (40 x y) + 0.25 (x^{2})$ .

$0.25 (40 x y + x^{2}) + 0.25 (400 y^{2})$

Factor $0.25$ out of $0.25 (40 x y + x^{2}) + 0.25 (400 y^{2})$ .

$0.25 (40 x y + x^{2} + 400 y^{2})$

Step 2

Factor using the perfect square rule.

Rearrange terms.

$0.25 (x^{2} + 40 x y + 400 y^{2})$

Rewrite $400 y^{2}$ as ${(20 y)}^{2}$ .

$0.25 (x^{2} + 40 x y + {(20 y)}^{2})$

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

$40 x y = 2 \cdot x \cdot (20 y)$

Rewrite the polynomial.

$0.25 (x^{2} + 2 \cdot x \cdot (20 y) + {(20 y)}^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 20 y$ .

$0.25 {(x + 20 y)}^{2}$