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Chapter 5: Problem 59

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

Short Answer

Expert verified
The product of the binomials is \(x^2 - 2x - 15\).

Step by step solution

01

Distribute the first term in the first binomial

First, distribute the \(x\) to the terms in the second binomial. This gives \(x \cdot x - x \cdot 5 = x^2 - 5x\).
02

Distribute the second term in the first binomial

Next, distribute the \(3\) to the terms in the second binomial. This gives \(3 \cdot x - 3 \cdot 5 = 3x - 15\).
03

Add the results of Steps 1 and 2

Finally, add the results of step 1 and step 2: \(x^2 - 5x + 3x - 15\). Concluding, the product of the two binomials is \(x^2 - 2x - 15\).

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Most popular questions from this chapter

Perform the indicated operations. $$(y+6)^{2}-(y-2)^{2}$$

Explain the difference between performing these two operations: $$2 x^{2}+3 x^{2} \text { and }\left(2 x^{2}\right)\left(3 x^{2}\right)$$

In Exercises \(79-82,\) simplify each expression. $$\left(\frac{9 x^{3}+6 x^{2}}{3 x}\right)-\left(\frac{12 x^{2} y^{2}-4 x y^{2}}{2 x y^{2}}\right)$$

In Exercises \(85-86,\) the variable \(n\) in each exponent represents a natural Number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

Explain how to multiply polynomials when neither is a monomial. Give an example.
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