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Chapter 1: Problem 44

\((-4 h)(-7 h)\)

Short Answer

Expert verified
The product is \(28h^2\).

Step by step solution

01

Identify the terms

The given expression is \((-4h)(-7h)\). Identify the first term, \(-4h\), and the second term, \(-7h\).
02

Apply the multiplication rule for coefficients

Multiply the coefficients: \(-4\) and \(-7\). Remember that the product of two negative numbers is positive: \(-4 \times -7 = 28\).
03

Multiply the variable parts

The variables in both terms are \(h\). By multiplying them, you apply the rule \(h \times h = h^2 \).
04

Combine the products

Combine the results from the previous steps to get the final product: \(28h^2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coefficients
In the expression \((-4 h)(-7 h)\), the numbers -4 and -7 are called coefficients. A coefficient is the numerical part of a term that is multiplied by a variable. In this exercise, the coefficients are -4 for the first term and -7 for the second term.

When multiplying expressions, you multiply the coefficients together as a separate step from the variables.

Here, you multiply \(-4 \times -7 = 28\). It's important to handle coefficients correctly to avoid mistakes in calculations.
Variables
Variables are symbols used to represent unknown values. In the given expression \((-4 h)(-7 h)\), the variable is \(h\).

When you multiply variables, you follow certain rules. The most important one is the rule of exponents: \(h \times h = h^2\).

This rule states that multiplying a variable by itself results in raising the variable to the next higher power.
Product of Negative Numbers
Multiplying negative numbers can be tricky, but there's a straightforward rule: the product of two negative numbers is positive.

In the exercise \((-4 h)(-7 h)\), both coefficients (-4 and -7) are negative. When we multiply them, the result is positive: \-4 \times -7 = 28\.

This is because multiplying two negatives cancels each other out, resulting in a positive number.
Exponents
Exponents show how many times a number is multiplied by itself. In the expression \((-4 h)(-7 h)\), each term has the variable \(h\) raised to the power of one (implicitly).

When you multiply \(h \times h\), you add the exponents: \(1+1 = 2\). This follows the rule \(a^m \times a^n = a^{m+n}\).

So, \(h \times h = h^2\). Therefore, the final expression becomes \(28h^2\).

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Most popular questions from this chapter

A market consists of four companies. Company A has \(30 \%\) of the market, Company B has \(10 \%\) of the market, Company C has \(10 \%\) of the market, and Company D has \(50 \%\) of the market. Find the HHI for this market.

The regular price of a 14 -piece cookware set is \(\$ 728\). It is on sale at a discount of \(35 \%\). The sales tax is \(6.5 \%\). Find the final cost of the cookware including tax. Round to the nearest hundredth.

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Find the circumference of a circle with a radius of \(0.7 \mathrm{in}\).

Find the volume of a cylinder with a radius of \(8 \mathrm{in}\). and height of 15 in.
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