Problem 44 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify the terms

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

Step 2: Apply the multiplication rule for coefficients

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

Step 3: Multiply the variable parts

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

Step 4: Combine the products

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

Key Concepts

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 \(28h^2\).