Middle School

Find the product of \(-3x^3\) and \((-2x^2 + 4x + 7)\).

A. \(6x^6 - 12x^4 + 21x^3\)
B. \(6x^5 - 12x^4 - 21x^3\)
C. \(6x^5 + 12x^4 + 21x^3\)

Answer :

For this case we must find the product of the following expression:[tex]-3x ^ 3 (-2x ^ 2 + 4x + 7)[/tex]

We apply distributive property to the terms within parentheses:

[tex](-3x ^ 3 * -2x ^ 2) + (- 3x ^ 3 * 4x) + (- 3x ^ 3 * 7) =[/tex]

We take into account that:

[tex]- * - = +\\- * + = -[/tex]

To multiply powers of the same base, put the same base and add the exponents.

[tex]6x ^ {3 + 2} -12x ^ {3 + 1} -21x ^ 3 =\\6x ^ 5-12x ^ 4-21x ^ 3[/tex]

Answer:

Option B