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Chapter 0: Problem 39

Find each product. $$\left(1-y^{5}\right)\left(1+y^{5}\right)$$

Short Answer

Expert verified
The result of the given exercise is \(1 - y^{10}\).

Step by step solution

01

Identify the formula

Identify the formula to use to simplify the multiplication. In this case, we use the difference of squares formula which is \(a^2 - b^2 = (a-b)(a + b)\).
02

Apply the formula

Apply the difference of squares formula to the given expressions. For this exercise, these are \(1 - y^{5}\) and \(1 + y^{5}\) Which are in the form \(a-b\) and \(a+b\) respectively. If we substitute these expressions into the formula, we have \((a - b)(a + b) = a^2 - b^2\), which becomes \((1 - y^{5})(1 + y^{5}) = 1^2 - (y^{5})^2\).
03

Finish the calculation

Evaluate \(1^2\) and \((y^{5})^2\), then subtract the square of \(y^{5}\) from the square of 1, we have \(1 - y^{10}\).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ x^{2}+36-(x+6)^{2} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Special-product formulas have patterns that make their multiplications quicker than using the FOIL method.

Factor completely. $$ x^{4}-y^{4}-2 x^{3} y+2 x y^{3} $$

Simplify using properties of exponents. $$\left(125 x^{9} y^{6}\right)^{3}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
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