/*! 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 82 Multiply. $$ (x+2)^{2} $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 82

Multiply. $$ (x+2)^{2} $$

Short Answer

Expert verified
Combine \( (x+2) \times (x+2) \) to get \( x^2 + 4x + 4 \).

Step by step solution

01

Understand the Task

The exercise requires expanding the expression \( (x+2)^2 \). This means multiplying \( (x+2) \) by itself.
02

Write the Expression Twice

Express the square as a product of two binomials: \( (x+2) \times (x+2) \).
03

Apply the FOIL Method

Use the FOIL (First, Outer, Inner, Last) method to multiply the binomials. Multiply each term in the first binomial by each term in the second binomial: - First: \( x \times x = x^2 \) - Outer: \( x \times 2 = 2x \) - Inner: \( 2 \times x = 2x \) - Last: \( 2 \times 2 = 4 \)
04

Combine Like Terms

Add the results of the FOIL method: \( x^2 + 2x + 2x + 4 \). Combine the middle terms \( 2x \) and \( 2x \): \( x^2 + 4x + 4 \).

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, Last. These represent the terms you multiply together when expanding an expression.
  • First: Multiply the first terms in each binomial.
  • Outer: Multiply the outer terms in the binomials.
  • Inner: Multiply the inner terms.
  • Last: Multiply the last terms in each binomial.
Let's apply the FOIL method to our example \((x+2)(x+2)\). Here's how it breaks down: 1. First: Multiply the first terms: \(x \times x = x^2\). 2. Outer: Multiply the outer terms: \(x \times 2 = 2x\). 3. Inner: Multiply the inner terms: \(2 \times x = 2x\). 4. Last: Multiply the last terms: \(2 \times 2 = 4\).You should now have these four products: \( x^2\), \(2x\), \(2x\), and \(4\).By following these steps, you systematically multiply each part of the binomials.
Expanding Expressions
Expanding expressions is all about breaking down a product of binomials into a sum of simpler terms. It converts the expression from a compact, factored form into a more spread-out form that can be easier to work with in further calculations. For our example \((x+2)^2\), this means turning \( (x+2) \times (x+2) \) into a sum of individual terms. After applying the FOIL method, you get the parts \( x^2\), \(2x\), \(2x\), and \(4\).Here鈥檚 a step-by-step breakdown:
  • First Term: \( x^2 \)
  • Second Term: \( 2x \)
  • Third Term: \( 2x \)
  • Fourth Term: \( 4 \)
These are your expanded terms. The expression is now spread out, showing every part clearly.
Combining Like Terms
Combining like terms simplifies expressions by merging terms that have the same variable raised to the same power. In the example \((x+2)^2\), after expanding we have: \(x^2 + 2x + 2x + 4\).Here, we notice two like terms: \(2x\) and \(2x\). These are terms with the same variable (\(x\)) raised to the same power (to the first power). To combine them, simply add their coefficients (the numbers in front of the variable): \ 2x + 2x = 4x \ .After combining, the simplified expression becomes: \ x^2 + 4x + 4 \.Combining like terms helps to keep algebraic expressions clean and easy to understand, making further calculations simpler.

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

Factor completely. Remember to look first for a common factor. If a polynomial is prime, state this. $$ 6 x^{2}-6 y^{2} $$

Review multiplying binomials using FOIL $$ (x+2)(x-7) $$

Factor completely. Assume that variables in exponents represent positive integers. $$ x^{2 a}-y^{2} $$

Factor completely. Assume that variables in exponents represent positive integers. $$ x^{8}-2^{8} $$

Solve. Round any irrational solutions to the nearest thousandth. $$ 3 x^{2}+x-1=0 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.