Problem 32
Question
Find each product. $$(x+5)(x-5)$$
Step-by-Step Solution
Verified Answer
The product of the expressions \((x+5)(x-5)\) equals to: \(x^2 - 25\).
1Step 1: Recognizing The Product Pattern
First, note that this problem can be solved using the formula for the difference of squares. The difference of squares formula is: \(a^2-b^2 = (a+b)(a-b)\). In the exercise, however, the form is applied in reverse, the term \(x\) takes the place of \(a\) and \(5\) takes place of \(b\).
2Step 2: Apply The Product
Applying the values of \(a\) and \(b\) to the difference of squares formula will give: \((a+b)(a-b) = a^2 - b^2\). Substituting the values from the equation, \(x + 5\) for \(a+b\) and \(x - 5\) for \(a-b\), you get the product: \(x^2 - 5^2\).
3Step 3: Solving The Expression
The last step is to finish the calculation. Square the current \(b\) which is \(5\) to get \(25\). Thus you get: \(x^2 - 25\) as result.
Other exercises in this chapter
Problem 32
Multiply or divide as indicated. $$\frac{x^{3}-25 x}{4 x^{2}} \cdot \frac{2 x^{2}-2}{x^{2}-6 x+5} \div \frac{x^{2}+5 x}{7 x+7}$$
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Factor each trinomial, or state that the trinomial is prime. $$ 9 x^{2}+5 x-4 $$
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Simplify each exponential expression in Exercises 23–64. $$\left(x^{11}\right)^{5}$$
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Find the union of the sets. \(\\{0,1,3,5\\} \cup\\{2,4,6\\}\)
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