Question

How would the sum of cubes formula be used to factor x^3y^3+343? Do not write the factorization

Answer 1

`\large\boxed{x^3y^3+343=(xy+7)(x^2y^2-7xy+49)}`

Explanation:

`x^3y^3=(xy)^3\\\\343=7^3\\\\x^3y^3+343=(xy)^3+7^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(xy+7)\bigg((xy)^2-(xy)(7)+7^2\bigg)=(xy+7)(x^2y^2-7xy+49)`