Factor 100x^10-60a^4x^5y^6+9a^8y^12

$100 x^{10} - 60 a^{4} x^{5} y^{6} + 9 a^{8} y^{12}$

Step 1

Rewrite $100 x^{10}$ as ${(10 x^{5})}^{2}$ .

${(10 x^{5})}^{2} - 60 a^{4} x^{5} y^{6} + 9 a^{8} y^{12}$

Step 2

Rewrite $9 a^{8} y^{12}$ as ${(3 a^{4} y^{6})}^{2}$ .

${(10 x^{5})}^{2} - 60 a^{4} x^{5} y^{6} + {(3 a^{4} y^{6})}^{2}$

Step 3

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

$60 a^{4} x^{5} y^{6} = 2 \cdot (10 x^{5}) \cdot (3 a^{4} y^{6})$

Step 4

Rewrite the polynomial.

${(10 x^{5})}^{2} - 2 \cdot (10 x^{5}) \cdot (3 a^{4} y^{6}) + {(3 a^{4} y^{6})}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 10 x^{5}$ and $b = 3 a^{4} y^{6}$ .

${(10 x^{5} - 3 a^{4} y^{6})}^{2}$