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Chapter 5: Problem 64

Find each product. In each case, neither factor is a monomial. $$(3 x-4)(x+5)$$

Short Answer

Expert verified
The product of \((3 x-4)(x+5)\) is \(3x^2 + 11x - 20\).

Step by step solution

01

Apply Distributive Property

First, the Distributive Property needs to be applied. This means that each term in the first binomial \(3x - 4\) is to be multiplied by each term in the second binomial \(x + 5\). The produced terms are \(3x * x\), \(3x * 5\), \(-4 * x\), and \(-4 * 5\).
02

Perform the multiplication

Now, multiply each pair of terms together. \(3x * x\) becomes \(3x^2\), \(3x * 5\) becomes \(15x\), \(-4 * x\) becomes \(-4x\), and \(-4 * 5\) becomes \(-20\). So the produced terms are \(3x^2\), \(15x\), \(-4x\), and \(-20\).
03

Combine Like Terms

The last step is to combine like terms. The terms \(15x\) and \(-4x\) are like terms and can be combined. Adding them together results in \(11x\). So, the final expression after combining like terms is \(3x^2 + 11x - 20\).

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