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Chapter 0: Problem 37

Find each product. $$\left(4 x^{2}+5 x\right)\left(4 x^{2}-5 x\right)$$

Short Answer

Expert verified
The product is \(16x^{4} - 25x^{2}\)

Step by step solution

01

Apply the distributive property

Multiply the first terms in each binomial, the outer terms, the inner terms, and then finally the last terms. So you would have \(4x^{2} * 4x^{2}, 4x^{2} * -5x, 5x * 4x^{2}, 5x * -5x\)
02

Calculate the products

Then, compute each of these products to get \(16x^{4}, -20x^{3}, 20x^{3}, -25x^{2}\)
03

Simplify

Combine like terms, which in this case are \(-20x^{3} + 20x^{3}\). These cancel out to give 0. Thus the final expression is \(16x^{4} - 25x^{2}\)

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Most popular questions from this chapter

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