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Chapter 5: Problem 38

Find each product of the monomial and the polynomial. $$x(x-7)$$

Short Answer

Expert verified
The product of the monomial and the polynomial \(x(x-7)\) is \(x^2 - 7x\).

Step by step solution

01

Identify the Monomial and the Polynomial

The given expression is \(x(x-7)\). Here, \(x\) is the monomial and \(x - 7\) is the polynomial.
02

Apply the Distributive Property

The distributive property states that \(a(b + c) = ab + ac\). Similarly, we can apply this property to our expression, \(x(x - 7) = x * x - x * 7\).
03

Perform the Multiplication

Multiplying the terms, we get \(x^2 - 7x\).
04

Simplify the Expression

Since there are no like terms, the expression \(x^2 - 7x\) is already in its simplest form.

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Most popular questions from this chapter

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

Explain the difference between \((-7)^{0}\) and \(-7^{0}\).

List the whole numbers in this set: $$\left\\{-4,-\frac{1}{5}, 0, \pi, \sqrt{16}, \sqrt{17}\right\\}$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x+4)\) b. \((x+5)(x+20)\)

Perform the indicated operations. $$(x+5)(x-6)-(x+2)(x-9)$$
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