/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 193 Multiply the following binomials... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 193

Multiply the following binomials. Use any method. $$(v+12)(v-5)$$

Short Answer

Expert verified
\((v+12)(v-5) = v^2 + 7v - 60\)

Step by step solution

01

Apply the FOIL Method

FOIL stands for First, Outer, Inner, and Last. Multiply each pair of terms in the binomials. First: Multiply the first terms: \(v \times v = v^2\)Outer: Multiply the outer terms: \(v \times (-5) = -5v\)Inner: Multiply the inner terms: \(12 \times v = 12v\)Last: Multiply the last terms: \(12 \times (-5) = -60\)
02

Combine Like Terms

Add the results of each multiplication: \(v^2 - 5v + 12v - 60\)
03

Simplify the Expression

Combine the like terms (the linear terms): \(v^2 + 7v - 60\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

FOIL method
The FOIL method is a handy way to multiply two binomials. FOIL stands for First, Outer, Inner, and Last. This acronym helps you remember the order in which you should multiply the terms of the binomials.
Imagine you have two binomials: \( (a + b)(c + d) \). Using the FOIL method, you do the following:
  • First: Multiply the first terms in each binomial: \( a \times c \)
  • Outer: Multiply the outer terms: \( a \times d \)
  • Inner: Multiply the inner terms: \( b \times c \)
  • Last: Multiply the last terms in each binomial: \( b \times d \)
For our exercise, the binomials are \( (v + 12)(v - 5) \):
1. \( v \times v = v^2 \) (First)
2. \( v \times (-5) = -5v \) (Outer)
3. \( 12 \times v = 12v \) (Inner)
4. \( 12 \times (-5) = -60 \) (Last)
This method ensures you cover all possible pairs of terms.
Combining Like Terms
Once you've used the FOIL method to multiply the binomials, you'll end up with several terms that need to be combined. In algebra, like terms have the same variable raised to the same power.
In our exercise, after using the FOIL method, we get: \( v^2 - 5v + 12v - 60 \).
Notice that \( -5v \) and \( 12v \) are like terms because they both contain the variable \( v \)

To combine them:
  • Add or subtract their coefficients: \(-5 + 12 = 7\)
Returning to our expression, we now write:
\( v^2 + 7v - 60 \.\) Oftentimes, combining like terms makes the expression simpler and easier to work with or understand.
Simplifying Expressions
The final step in multiplying binomials is simplifying the expression. Simplifying means to reduce the expression to its most concise form.
From our example, we left off at: \( v^2 + 7v - 60 \). This is already simplified because:
  • There are no more like terms to combine
  • The expression is in standard polynomial form: first the term with the highest exponent, then in decreasing order of the exponents.
Sometimes, simplifying might involve factoring or other methods, but in this case, combining like terms was all that was needed.
Always double-check your final expression to make sure each term is in its simplest form and all like terms have been appropriately combined. This will ensure your solution is correct and easy to interpret!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Convert \(5.25 \times 10^{-4}\) to decimal form.

Divide the monomials. $$\frac{11 u^{6} v^{3}}{55 u^{2} v^{8}}$$

Simplify. $$x^{-3} \cdot x^{9}$$

Simplify. $$\left(\frac{3}{5}\right)^{2}$$

Write each number in scientific notation. $$5,300,000$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.