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Chapter 5: Problem 62

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 the given binomials is \(49x^2y^4-100y^2\).

Step by step solution

01

Identify the structure

First, we can see that the binomials \((7xy^2-10y)\) and \((7xy^2+10y)\) are conjugates of each other. Knowing this, we can use the formula to simplify the multiplication.
02

Apply formula for the product of conjugates

We then use the rule that the product of conjugates \((a-b)(a+b)=a^2-b^2\). Here \(a=7xy^2\) and \(b=10y\). Substituting these values into the formula we get the product as \(a^2-b^2 = (7xy^2)^2-(10y)^2\).
03

Simplify the squares

Now, simplify the terms by squaring them to get our answer. This results in \((7xy^2)^2-(10y)^2 = 49x^2y^4-100y^2\).

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