Factor 9x^8+6x^4(y+2)+(y+2)^2

$9 x^{8} + 6 x^{4} (y + 2) + {(y + 2)}^{2}$

Step 1

Rewrite $9 x^{8}$ as ${(3 x^{4})}^{2}$ .

${(3 x^{4})}^{2} + 6 x^{4} (y + 2) + {(y + 2)}^{2}$

Step 2

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

$6 x^{4} (y + 2) = 2 \cdot (3 x^{4}) \cdot (y + 2)$

Step 3

Rewrite the polynomial.

${(3 x^{4})}^{2} + 2 \cdot (3 x^{4}) \cdot (y + 2) + {(y + 2)}^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3 x^{4}$ and $b = y + 2$ .

${(3 x^{4} + y + 2)}^{2}$