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Find the product. Simplify your answer. $\newline$ $(2r + 1)(-4r^2 + 3r - 1)$

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Multiply polynomials

Full solution

Q. Find the product. Simplify your answer.

\newline

(2r + 1)(-4r^2 + 3r - 1)

Multiply with Second Trinomial: We start by multiplying $2r$ with each term in the second trinomial: $\newline$ $2r \times (-4r^2) = -8r^3$ $\newline$ $2r \times 3r = 6r^2$ $\newline$ $2r \times (-1) = -2r$
Combine Products: Next, we multiply $1$ with each term in the second trinomial: $\newline$ $1 \times (-4r^2) = -4r^2$ $\newline$ $1 \times 3r = 3r$ $\newline$ $1 \times (-1) = -1$
Combine Like Terms: Now, we combine the like terms from the two sets of products: $\newline$ $-8r^3$ (from $2r * -4r^2$ ) $\newline$ $6r^2$ (from $2r * 3r$ ) $\newline$ $-2r$ (from $2r * -1$ ) $\newline$ $-4r^2$ (from $1 * -4r^2$ ) $\newline$ $3r$ (from $1 * 3r$ ) $\newline$ $2r * -4r^2$ $0$ (from $2r * -4r^2$ $1$ )
Simplify Result: Adding the like terms together, we get: $\newline$ $-8r^3 + (6r^2 - 4r^2) + (-2r + 3r) - 1$ $\newline$ Which simplifies to: $\newline$ $-8r^3 + 2r^2 + r - 1$

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