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Chapter 0: Problem 36

Find each product. $$(4-3 x)(4+3 x)$$

Short Answer

Expert verified
The product of the given expressions is \( 16 - 9x^2 \)

Step by step solution

01

Apply the FOIL method

Starting with the expression \( (4-3x)(4+3x) \), apply the FOIL method. First, multiply the first terms in each parentheses: \( 4 * 4 = 16 \). Next, multiply the outer terms: \( 4 * 3x = 12x \). Then, multiply the inner terms: \( -3x * 4 = -12x \). Finally, multiply the last terms: \( -3x * 3x = -9x^2 \).
02

Combine like terms

Now, add the results together: \( 16 + 12x - 12x - 9x^2 \). Notice that the \( 12x \) and \( -12x \) cancel each other out.
03

Simplify the expression

After canceling terms, you are left with \( 16 - 9x^2 \). This is the final answer.

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