Question

Here’s an example of a polynomial expression that has more complicated expressions we’ll need to substitute for a and b. We’ll set it up to mirror the structure of the perfect cube identity.

In this expression, a is represented by
and b is represented by
.

As we substitute
for a and
for b in the identity, we need to be careful to substitute exactly. For example, we don’t want to confuse the coefficient or the exponent in the b-term for exponents in the identity.

Next, simplify using the properties of exponents and multiplication to get the simplified expanded form. Look closely: this form mirrors the perfect trinomial identity with its own values for a and b.

Answer 1

`(2x + 3y^(2)) (2x + 3y^(2) )^(2)`

Explanation:

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