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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 is: \(4 - y^{10}\).

Step by step solution

01

Recognize the pattern

Recognize that the given expression fits the pattern of a difference of squares, \(a^2 - b^2\), which can be factored as \((a - b)(a + b)\). In this case, \(a = 2\) and \(b = y^{5}\).
02

Apply the formula

Apply the formula of difference of squares to the given expression. This results in the following: \((2 - y^{5})(2 + y^{5}) = a^2 - b^2 = 2^2 - (y^{5})^2\).
03

Simplify the equation

Simplify the equation by performing the relevant mathematical operations which results in the following: \(4 - y^{10}\).

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Most popular questions from this chapter

Explain how to factor $$x^{3}+1$$

Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \% .\) Now the sale price is reduced by another \(30 \%\). If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?

Find all integers \(b\) so that the trinomial can be factored. $$x^{2}+b x+15$$

What does it mean to factor completely?

Find the intersection of the sets. $$\\{a, b, c, d\\} \cap \varnothing$$
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