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Chapter 0: Problem 82

State the name of the property illustrated. $$-8(3+11)=-24+(-88)$$

Short Answer

Expert verified
The property illustrated in the exercise is the distributive property.

Step by step solution

01

Identify the property

Recognize the structure of the equation. There are two sides to the equation, on the left-hand side, a number is being multiplied by the sum of two other numbers (-8*(3+11)). On the right-hand side, there are two numbers being summed, which are the result of (-8*3) and (-8*11). This is the pattern of the distributive property of multiplication over the addition.
02

State the property

The property of distribution states that the multiplication of a number by the sum of two numbers is equal to the sum of the product of the number and each addend. Mathematically, for any a, b, and c, we have \(a*(b+c) = a*b + a*c\). This is exactly what's being demonstrated in this equation -8*(3+11) equals (-8*3) + (-8*11). Thus, the property illustrated in the equation is the distributive property.

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-6 x+3, \text { for } x=7$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The cube root of \(-8\) is not a real number.

$$\text { Factor completely.}$$ $$7 x^{4}+34 x^{2}-5$$

Explain how to factor $$3 x^{2}+10 x+8$$

This will help you prepare for the material covered in the next section. a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)
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