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Chapter 5: Problem 70

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

Short Answer

Expert verified
The product is \(x^{2}y^{2} - a^{2}b^{4}\)

Step by step solution

01

Identify the Binomials

Identify the binomials to be multiplied. Here it is \( (x y+a b^{2}) (x y- a b^{2})\)
02

Apply the Difference of Squares Formula

The problem is in the form of a difference of squares, \(a^{2} - b^{2} = (a+b)(a-b)\). Here \(a = xy\) and \(b = ab^{2}\) . The product of the binomials will be \(a^{2} - b^{2}\)
03

Calculate the Product

Finally, calculate the product: \(a^{2} - b^{2} = (xy)^{2} - (ab^{2})^{2} = x^{2}y^{2} - a^{2}b^{4}\)

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Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm working with two monomials that I cannot add, although I can multiply them.

Perform the indicated computations. Express answers in scientific notation. $$\left(2 \times 10^{2}\right)\left(2.6 \times 10^{-3}\right) \div\left(4 \times 10^{3}\right)$$

Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.

Explain the difference between \((-7)^{0}\) and \(-7^{0}\).

Explain how to divide monomials. Give an example.
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