Problem 37 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(4x^{2} * 4x^{2}, 4x^{2} * -5x, 5x * 4x^{2}, 5x * -5x\)

Step 2: Calculate the products

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

Step 3: Simplify

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