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Chapter 6: Problem 111

Explain how to factor the difference of two squares. Provide an example with your explanation.

Short Answer

Expert verified
The difference of squares formula, \(a^2 - b^2 = (a + b)(a - b)\), can be applied to factor expressions. For example, \(5^2 - 4^2\) factors to \((5 + 4)(5 - 4)\), which simplifies to \((9)(1)\).

Step by step solution

01

Understanding the Difference of Squares

The difference of squares is a special algebraic identity for the expression in the form \(a^2 - b^2\). This expression can be factored into \( (a + b)(a - b)\) according to the formula.
02

Example Selection

To illustrate this, consider a simple concrete example where \(a = 5\) and \(b = 4\). This results in the expression \(5^2 - 4^2\).
03

Apply the Formula

The expression \(5^2 - 4^2\) can be rewritten as \((5 + 4) (5 - 4)\), according to the formula.
04

Simplification

Simplify the factored expression to obtain \((9) (1)\).

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Most popular questions from this chapter

Exercises \(137-139\) will help you prepare for the material covered in the next section. In each exercise, factor completely. $$2 x^{2}-20 x+50$$

Exercises \(150-152\) will help you prepare for the material covered in the next section. Evaluate \((3 x-1)(x+2)\) for \(x=\frac{1}{3}\)

In Exercises \(124-127,\) factor each polynomial. $$x^{2 n}-25 y^{2 n}$$

Make Sense? In Exercises \(115-118\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I factored \(9-25 x^{2}\) as \((3+5 x)(3-5 x)\) and then applied the commutative property to rewrite the factorization as \((5 x+3)(5 x-3)\)

Use the \(x\)-intercepts for the graph in \(a[-10,10,1]\) by \([-13,10,1]\) viewing rectangle to solve the quadratic equation. Check by substitution. Use the graph of \(y=(x-2)(x+3)-6\) to solve \((x-2)(x+3)-6=0\).
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