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Chapter 5: Problem 65

Find each product. In each case, neither factor is a monomial. $$\left(\frac{1}{4} x+4\right)\left(\frac{3}{4} x-1\right)$$

Short Answer

Expert verified
\(\frac{3}{16} x^2 +\frac{11}{4}x - 4\)

Step by step solution

01

Multiply the First Terms

Multiply the first terms in each binomial. In this case, multiply \(\frac{1}{4} x\) and \(\frac{3}{4} x\). That gives \(\frac{3}{16} x^2\).
02

Multiply the Outer Terms

Next, multiply the outer terms. These are \(\frac{1}{4} x\) and \(-1\). That gives \(-\frac{1}{4} x\).
03

Multiply the Inner Terms

Now, multiply the inner terms. These are \(4\) and \(\frac{3}{4} x\). This gives \(3x\).
04

Multiply the Last Terms

Lastly, multiply the last terms in each binomial. These are \(4\) and \(-1\). That gives \(-4\).
05

Combine Like Terms

Add the results from the previous steps together. The solution is \(\frac{3}{16} x^2 +\frac{11}{4}x - 4\).

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