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Chapter 0: Problem 72

Find each product. $$(7 x+3 y)(7 x-3 y)$$

Short Answer

Expert verified
The product of the given binomial expressions is \(49x^2 - 9y^2\)

Step by step solution

01

Applying the Formula

The given expression can be written as the difference of two squares, therefore, write the multiplication of two binomial expressions using formula \((a + b)(a - b) = a^2 - b^2\), where \(a = 7x\) and \(b = 3y\). Replace \(a\) and \(b\) in the formula.
02

Computing the Product

By substituting \(a = 7x\) and \(b = 3y\) into the difference of squares formula, we have \((7x)^2 - (3y)^2\).
03

Simplifying the Expression

Finally, simplify the obtained expression. This gives \(49x^2 - 9y^2\).

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Most popular questions from this chapter

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{4}}=-2$$

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

What is a linear equation in one variable? Give an example of this type of equation.

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.
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