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Chapter 0: Problem 32

Find each product. $$(x+5)(x-5)$$

Short Answer

Expert verified
The product of the binomials \( (x+5)(x-5) \) is \( x^2 - 25 \)

Step by step solution

01

Apply the Distributive Property

Begin by applying the distributive property, which states that multiplication distributes over addition and subtraction. This means that each term inside the first binomial \((x+5)\) must be multiplied by each term inside the second binomial \((x-5)\). Thus, we get four products initially: \(x * x, x*(-5), 5*x\) and \(5*(-5)\).
02

Simplify the Product

Simplify the expressions obtained from the distribution. The multiplication of \(x*x\) equals \(x^2\), \(x*(-5)\) equals \(-5x\), \(5*x\) equals \(5x\), and \(5*(-5)\) equals \(-25\). Now, our equation looks like this: \(x^2 - 5x + 5x - 25\)
03

Combine like terms

Combine all similar terms for final simplification. Notice that \(-5x\) and \(5x\) are like terms and can be added together. These terms will cancel out because they sum up to zero. Therefore, the simplified expression is \(x^2 - 25\)

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Most popular questions from this chapter

Find the union of the sets. $$\\{e, m, p, t, y\\} \cup \varnothing$$

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

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$

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