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Find the product. Simplify your answer. $\newline$ $(4n - 3)(-2n^2 - 4n + 2)$

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Multiply polynomials

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Q. Find the product. Simplify your answer.

\newline

(4n - 3)(-2n^2 - 4n + 2)

Distribute $4n$ : To find the product of two binomials, we will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first binomial by each term in the second binomial. $\newline$ First, we distribute $4n$ across the second binomial: $4n \times (-2n^2) + 4n \times (-4n) + 4n \times 2$ .
Calculate first part: Calculating the first part of the distribution: $4n \times (-2n^2) = -8n^3$ .
Calculate second part: Calculating the second part of the distribution: $4n \times (-4n) = -16n^2$ .
Calculate third part: Calculating the third part of the distribution: $4n \times 2 = 8n$ .
Distribute $-3$ : Now, we distribute $-3$ across the second binomial: $-3 \times (-2n^2) + -3 \times (-4n) + -3 \times 2$ .
Calculate first part: Calculating the first part of this distribution: $-3 \times (-2n^2) = 6n^2$ .
Calculate second part: Calculating the second part of this distribution: $-3 \times (-4n) = 12n$ .
Calculate third part: Calculating the third part of this distribution: $-3 \times 2 = -6$ .
Combine all terms: Now we combine all the terms we have calculated: $-8n^3 + (-16n^2) + 8n + 6n^2 + 12n - 6$ .
Combine like terms: We combine like terms: $-8n^3 + (-16n^2 + 6n^2) + (8n + 12n) - 6$ .
Simplify like terms: Simplifying the like terms: $-8n^3 - 10n^2 + 20n - 6$ .

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