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Chapter 0: Problem 82

Find each product. $$\left(7 x y^{2}-10 y\right)\left(7 x y^{2}+10 y\right)$$

Short Answer

Expert verified
The product of \((7xy^{2} - 10y)\) and \((7xy^{2} + 10y)\) is \(49x^{2}y^{4} - 100y^{2}\)

Step by step solution

01

Identify the formula pattern

The given problem can be seen as the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 7xy^{2}\) and \(b = 10y\).
02

Apply the formula

Using the formula, we simply square the first term and subtract the square of the second term: \(a^2 - b^2 = (7xy^{2})^2 - (10y)^2\).
03

Simplify the result

Square each term: \(49x^{2}y^{4} - 100y^{2}\).

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Most popular questions from this chapter

In Exercises \(11-16,\) factor by grouping. $$x^{3}-2 x^{2}+5 x-10$$

evaluate each algebraic expression for the given value of the variable or variables. $$ \frac{2 x+y}{x y-2 x} ; x=-2 \text { and } y=4 $$

In Exercises \(11-16,\) factor by grouping. $$x^{3}+6 x^{2}-2 x-12$$

state the name of the property illustrated. $$ 6+(-4)=(-4)+6 $$

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