Question

Factor this expression completely, and, then, place the factors in the proper location on the grid. Place the binomial factor first. x 3 + y 3

Answer 1

(x-y)(x^2+xy+y^2)
_______________

the first parentheses contain the cubed root of both the terms so x and y respectively. second parentheses follows the formula (a^2 + ab + b^2)
x corresponds to a and y corresponds to b. The signs are what change depending on what the original equation is. Since the original is a subtraction then the signs are -/+/+. you can remember it using the acronym SOAP. (S = same, O = opposite, AP = always positive) So the first sign is x - y (same as subtraction from original), the second and third are x^2 + xy + y^2 (opposite is a plus, and the last sign is always a positive)

Answer 2

`x^(3)+y^(3)=(a+b)(a^(2)-ab+b^(2))`

Explanation:

The given expression is

`x^(3)+y^(3)`

This expression represents the sum of two perfect cubes, which is factorize as this product

`x^(3)+y^(3)=(a+b)(a^(2)-ab+b^(2))`

We can demonstrate this factorization by multiplying the product

`(a+b)(a^(2)-ab+b^(2))=a^(3)-a^(2)b+ab^(2)+a^(2)b-ab^(2)+b^(3)=a^(3)+b^(3)`

Therefore, the answer is

`x^(3)+y^(3)=(a+b)(a^(2)-ab+b^(2))`