Question

Multiply the binomials. $\left(5 x^3+x^2\right)\left(4 x^2-3\right)$

   Multiply the binomials.
$\left(5 x^3+x^2\right)\left(4 x^2-3\right)$

Intermediate Algebra

Intermediate Algebra

Lisa Healey 1st Edition

Chapter 4, Problem 23

Instant Answer

Solved by Expert Maninder Singh

07/27/2020

Step 1

Step 1: Identify the binomials to be multiplied: \((5x^3 + x^2)\) and \((4x^2 - 3)\). Show more…

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Multiply the binomials. $\left(5 x^3+x^2\right)\left(4 x^2-3\right)$

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Key Concepts

Distributive Property

The distributive property allows the multiplication of a sum by distributing the multiplication over each addend. In the context of polynomials, this property justifies the step-by-step multiplication of each term in the first polynomial with each term in the second polynomial.

Polynomial Multiplication

Polynomial multiplication involves multiplying two or more polynomial expressions to yield another polynomial. This is done by multiplying each term in one polynomial by each term in the other and then combining like terms, ensuring that all possible product combinations are considered.

Laws of Exponents

When multiplying terms with the same base, the laws of exponents are applied, specifically by adding the exponents. This rule is crucial in simplifying the product of polynomial terms that involve variables raised to different powers.

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