Question

Multiply the polynomials. $$(6 x-1)(5+2 x)$$

Name: Problem 19, Chapter 4: Intermediate Algebra
Uploaded: 2020-06-18T11:10:29-08:00
Duration: 1 min 10 s
Channel: Ankit Gupta
Description: Multiply the polynomials. (6 x-1)(5+2 x)

   Multiply the polynomials.
$$(6 x-1)(5+2 x)$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 4, Problem 19

Instant Answer

Solved by Expert Ankit Gupta

06/18/2020

Step 1

This gives us: \[6x \cdot 5 + 6x \cdot 2x - 1 \cdot 5 - 1 \cdot 2x\] Show more…

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Multiply the polynomials. $$(6 x-1)(5+2 x)$$

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Key Concepts

Polynomial Multiplication

Polynomial multiplication involves multiplying two or more polynomials together. This process requires applying the distributive property to ensure that every term in one polynomial is multiplied by each term in the other polynomial, resulting in a new, typically higher-degree, polynomial.

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. In the context of polynomial multiplication, it ensures that each term from the first polynomial is distributed across all terms in the second polynomial.

Combining Like Terms

After the multiplication process, it is necessary to combine like terms—terms that have the same variables raised to the same powers—in order to simplify the expression. This step consolidates the polynomial into its simplest and most organized form.

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