Question

Multiply the polynomials. $$(2 a+b)(5 a-3)$$

   Multiply the polynomials.
$$(2 a+b)(5 a-3)$$

Prealgebra

Julie Miller, Molly… 1st Edition

Chapter 10, Problem 33

Instant Answer

Solved by Expert Maninder Singh

07/26/2020

Step 1

This gives us: \[2a(5a) + 2a(-3) + b(5a) + b(-3)\] Show more…

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Multiply the polynomials. $$(2 a+b)(5 a-3)$$

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Key Concepts

Combining Like Terms

After expanding the product of polynomials, like terms—terms with the same variables and exponents—can be combined to simplify the expression. This step is crucial for presenting the result in its most reduced and comprehensible form.

Distributive Property

This property allows one to multiply a single term by a sum or difference, distributing the multiplication across each term inside the parentheses. It forms the foundation for expanding products of expressions, as it ensures every term in one polynomial is multiplied by every term in the other.

Binomial Multiplication

Binomial multiplication is a specific application of the distributive property when multiplying two expressions, each containing two terms. Techniques like the FOIL method (First, Outer, Inner, Last) are often used to systematically perform this multiplication.

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