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Chapter 5: Problem 49

Find each product. $$ (3 a+2 c)(3 a-2 c) $$

Short Answer

Expert verified
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Step by step solution

01

Identify the formula

Recognize that the given expression i.e., i.e., i.e., i.e., i.e., can be expressed in the form of i.e., i.e.,
02

Apply the formula

The difference of squares formula states that Using this formula, substitute and or in this problem, we get: Then, i.e., Therefore: i.e.,
03

Simplify the expression

Finally, simplifyto get: or or Therefore, the simplified product is:

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Key Concepts

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

Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operations like addition, subtraction, multiplication, and division. For instance, in our exercise, \((3a + 2c)\) and \((3a - 2c)\) are algebraic expressions. These expressions involve variables \a\ and \c\ and constants \3\ and \2\. Knowing how to work with algebraic expressions is crucial because they form the foundation of algebra.

When dealing with them, remember to:
  • Identify and group like terms - terms with the same variable and exponent.
  • Apply rules of arithmetic consistently.
Multiplication of Binomials
The multiplication of binomials is a key algebraic skill. A binomial is a polynomial with exactly two terms. In the given exercise, \((3a + 2c)\) and \((3a - 2c)\) are binomials. When multiplying binomials, you often use formulas to simplify the process.

In this case, the binomials fit the \

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Most popular questions from this chapter

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ -4 r^{-2}\left(r^{4}\right)^{2} $$

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In Exercises 65鈥�74, the factors involve fractions or decimals. Apply the methods of this sec- tion, and find each product. $$ \left(3 w+\frac{1}{4} z\right)(w-2 z) $$
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