Problem 201 Multiply the following binomials... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 201

Multiply the following binomials. Use any method. $$(3 u-8)(5 u-14)$$

Short Answer

Expert verified

15u^2 - 82u + 112

Step by step solution

- Apply the FOIL Method

Use the FOIL method to multiply the binomials. FOIL stands for First, Outer, Inner, Last terms.First: Multiply the first terms of each binomial: $ (3u)(5u) = 15u^2 $Outer: Multiply the outer terms of each binomial: $ (3u)(-14) = -42u $Inner: Multiply the inner terms of each binomial: $ (-8)(5u) = -40u $Last: Multiply the last terms of each binomial: $ (-8)(-14) = 112 $

- Combine Like Terms

Add the results of the Outer and Inner multiplications from the previous step to combine like terms: $ -42u - 40u = -82u $

- Assemble the Polynomial

Combine the results of all parts (First, combined Outer+Inner, and Last) to write the final polynomial: $ 15u^2 - 82u + 112 $

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

FOIL Method

The FOIL method is a shortcut for multiplying two binomials. The acronym stands for First, Outer, Inner, Last. It's a way to remember the order in which to multiply the terms.
First, you multiply the first term of each binomial: $ (3u)(5u) = 15u^2 $. This gives you the first term of the resulting polynomial. Next are the outer terms: $ (3u)(-14) = -42u $, followed by the inner terms: $ (-8)(5u) = -40u $. Lastly, you multiply the last terms of both binomials: $ (-8)(-14) = 112 $. By following these steps, you ensure that all the terms are correctly multiplied.

Polynomial

A polynomial is an expression consisting of variables and coefficients, connected by addition, subtraction, and multiplication. In the solution, multiplying the binomials resulted in the polynomial $ 15u^2 - 82u + 112 $. This polynomial has three parts:
1. The quadratic term: $ 15u^2 $. The variable $u$ is raised to the second power.
2. The linear term: $ -82u $. The variable $u$ appears to the first power.
3. The constant term: $ 112 $. This term has no variables.
By combining these, we form the complete polynomial expression.

Combining Like Terms

In mathematics, 'like terms' are terms that have the same variable raised to the same power. When multiplying binomials, you often end up with multiple like terms that need to be simplified.
For example, during the FOIL method, you get $ -42u $ from the outer terms and $ -40u $ from the inner terms. Both of these are like terms because they both have the variable $u$ raised to the first power. Combining them, $ -42u - 40u = -82u $, simplifies the expression.
Combining like terms is important because it reduces the polynomial to its simplest form, making it easier to work with for further operations or analyses.

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91影视

Multiply the following binomials. Use any method. $$(3 u-8)(5 u-14)$$

Short Answer

Step by step solution

- Apply the FOIL Method

- Combine Like Terms

- Assemble the Polynomial

Key Concepts

FOIL Method

Polynomial

Combining Like Terms

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