Question

Multiply the polynomials. $$(4 m-13)\left(2 m^{2}-7 m+9\right)$$

   Multiply the polynomials.
$$(4 m-13)\left(2 m^{2}-7 m+9\right)$$

Algebra and Trigonometry

Algebra and Trigonometry

Jay Abramson 1st Edition

Chapter 1, Problem 44

Instant Answer

Solved by Expert Grace Muhihu

07/11/2020

Step 1

This means multiplying each term in the first polynomial by each term in the second polynomial. So, we have: \[4m \cdot (2m^2 - 7m + 9) - 13 \cdot (2m^2 - 7m + 9)\] Show more…

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Multiply the polynomials. $$(4 m-13)\left(2 m^{2}-7 m+9\right)$$

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Key Concepts

Distributive Property

A core algebraic principle that enables the multiplication of a term across a sum or difference. In polynomial multiplication, it ensures that each term of one polynomial is correctly multiplied by each term of the other.

Combining Like Terms

After expansion, similar terms—those with the same variable parts and exponents—are consolidated to simplify the expression. This process is essential for arriving at the most reduced form of the polynomial.

Polynomial Multiplication

This concept involves multiplying each term of one polynomial by each term of another, ensuring that all products are accounted for. It is fundamental in algebra when dealing with the expansion or simplification of expressions.

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