Question

Multiply the binomials. $\left(3 d^2-5 d\right)\left(2 d^2+9\right)$

   Multiply the binomials.
$\left(3 d^2-5 d\right)\left(2 d^2+9\right)$

Intermediate Algebra

Intermediate Algebra

Lisa Healey 1st Edition

Chapter 4, Problem 22

Instant Answer

Solved by Expert Julie Silva

03/24/2021

Step 1

Step 1: Identify the binomials to be multiplied: \((3 d^2 - 5 d)\) and \((2 d^2 + 9)\). Show more…

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Multiply the binomials. $\left(3 d^2-5 d\right)\left(2 d^2+9\right)$

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Key Concepts

Polynomial Multiplication

This is a process where each term of one polynomial is multiplied by every term of the other polynomial. It involves using algebraic techniques to systematically combine terms from the two polynomials, ensuring that all possible products are considered.

Distributive Property

The distributive property is a fundamental algebraic property that allows you to multiply a sum by multiplying each addend individually by the multiplier and then summing the results. This property underpins the method of multiplying polynomials.

Combining Like Terms

After multiplication, the resulting expression may include several terms that have the same variable raised to the same power. Combining like terms involves adding or subtracting these similar terms to simplify the expression into a more concise form.

Binomials

Binomials are polynomials that consist of exactly two terms. Multiplying binomials introduces the concept of handling multiple terms and requires careful application of the distributive property to ensure each term is correctly multiplied.

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