Question

1. Create an expression, containing at least two variables, that can be factored using the sum of two cubes identity.

Show the factored form of the expression, then verify that it is equivalent to the original expression.

Answer 1

Remember that the sum of tow cubes identity is:
`a^3+b^3=(a+b)(a^2-ab+b^2)`
So, to create our expression, containing at least two variables, that can be factored using the sum of two cubes, we just need to replace
`a` and
`b` with tow monomials with a different variable:

`a=x` and
`b=y`
Lets replace those values in our identity:

`x^3+y^3`

Now that we have our expression, lets factor it using the sum of two cubes identity:

`x^3+y^3=(x+y)(x^2-xy+y^2)`
To verify if the factored form of our expression (right hand side) is equivalent to the original form (left hand side), we are going to expand the right hand side:

`x^3+y^3=(x+y)(x^2-xy+y^2)`

`x^3+y^3=x^3-x^2y+xy^2+x^2y-xy^2+y^3`

`x^3+y^3=x^3+x^2y-x^2y+xy^2-xy^2+y^3`

`x^3+y^3=x^3+y^3`

Since both sides of the equation are equal, we can conduce that the factored form of our expression is equivalent to the original expression.