Question

multiply the polynomials using the foil method. combine like terms.

\\x(5x^3 + 8)(5x^3 - 8)\\

Explanation:

Identify the expression and strategy

We are given the expression:

$$ x(5x^3 + 8)(5x^3 - 8) $$

We need to multiply the polynomials. We can first multiply the two binomials \((5x^3 + 8)(5x^3 - 8)\) using the FOIL Method or recognize them as a Difference of Squares, and then multiply the resulting polynomial by the monomial \(x\).

Multiply the binomials

Using the FOIL Method knowledge point:

$$
LATEXBLOCK0
$$

Combine like terms

Using the Difference of Squares knowledge point:

$$
LATEXBLOCK1
$$

Distribute the monomial

Using the Multiplying Monomial by Polynomial knowledge point:

$$
LATEXBLOCK2
$$

Answer:

\(25x^7 - 64x\)