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Chapter 0: Problem 38

Find each product. $$\left(3 x^{2}+4 x\right)\left(3 x^{2}-4 x\right)$$

Short Answer

Expert verified
The product of the given binomials is \(9x^{4} - 16x^{2}\)

Step by step solution

01

Identify Binomials

First, identify the given expressions as binomials. Given binomials are \((3x^{2} + 4x)\) and \((3x^{2} - 4x)\)
02

Apply FOIL Method

Apply the FOIL method on these binomials. Following are the terms obtained after applying FOIL:First: Multiplication of the first terms in each binomial (\(3x^{2} * 3x^{2}\)), which is \(9x^{4}\),Outer: Multiplication of the outer terms in the binomials (\(3x^{2} * -4x\)), which is \(-12x^{3}\),Inner: Multiplication of the inner terms in the binomials (\(4x * 3x^{2}\)), which is \(12x^{3}\),Last: Multiplication of the last terms in each binomial (\(4x * -4x\)), which is \(-16x^{2}\).Therefore, FOIL method gives us \(9x^{4} -12x^{3} +12x^{3} -16x^{2}\)
03

Combine Like Terms

Combine like terms. The terms containing \(x^{3}\) can be combined:\(9x^{4} -12x^{3} + 12x^{3} - 16x^{2}= 9x^{4} - 16x^{2}\)

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$y^{7}+y$$

This will help you prepare for the material covered in the next section. a. Find \(\sqrt{16} \cdot \sqrt{4}\) b. Find \(\sqrt{16 \cdot 4}\) c. Based on your answers to parts (a) and (b), what can you conclude?

$$\frac{1}{2}+\frac{2}{3}$$

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