Algebra Examples

${(x - 5)}^{2} + 2 y^{3} (x - 5) + y^{6}$

Step 1

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

${(x - 5)}^{2} + 2 y^{3} (x - 5) + {(y^{3})}^{2}$

Step 2

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

$2 y^{3} (x - 5) = 2 \cdot (x - 5) \cdot y^{3}$

Step 3

Rewrite the polynomial.

${(x - 5)}^{2} + 2 \cdot (x - 5) \cdot y^{3} + {(y^{3})}^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x - 5$ and $b = y^{3}$ .

${(x - 5 + y^{3})}^{2}$