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Chapter 0: Problem 40

Find each product. $$\left(2-y^{5}\right)\left(2+y^{5}\right)$$

Short Answer

Expert verified
The product of \( \left(2-y^{5}\right)\left(2+y^{5}\right) \) is \( 4 - y^{10} \).

Step by step solution

01

Identify The Difference of Squares

The given expression is \( \left(2-y^{5}\right)\left(2+y^{5}\right) \). This is of the form \( (a - b)(a + b) \), which is a pattern for the difference of squares.
02

Use The Difference of Squares Formula

We can use the formula of difference of squares to multiply this expression. The formula is \( (a - b)(a + b) = a^{2} - b^{2} \). Replace \( a \) with \( 2 \) and \( b \) with \( y^{5} \) in this formula.
03

Compute The Square of \( a \) And \( b \)

Calculate the square of \( a \) and \( b \). We get \( a^{2} = 2^{2} = 4 \) and \( b^{2} = (y^{5})^{2} = y^{10} \).
04

Substitute The Values

Substitute the calculated squares of \( a \) and \( b \) into the formula. We get the expression: \( 4 - y^{10} \).

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Most popular questions from this chapter

Use the quotient rule to simplify the expressions in Exercises \(17-26 .\) Assume that \(x>0\) $$\frac{\sqrt{24 x^{4}}}{\sqrt{3 x}}$$

Use the product rule to simplify the expressions in Exercises \(7-16 .\) In Exercises \(11-16,\) assume that variables represent nonnegative real numbers. $$\sqrt{10 x} \cdot \sqrt{8 x}$$

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{x^{2}+12 x+36}{x^{2}-36} $$

Use the quotient rule to simplify the expressions in Exercises \(17-26 .\) Assume that \(x>0\) $$\sqrt{\frac{1}{81}}$$

In Exercises \(1-10\), factor out the greatest common factor. $$x^{2}(2 x+5)+17(2 x+5)$$
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