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Chapter 5: Problem 53

Find each product. $$(3 x+y)(3 x-y)$$

Short Answer

Expert verified
The product of \((3x + y)(3x - y)\) is \(9x^2 - y^2\)

Step by step solution

01

Apply the difference of squares formula

Given the expression is \((3x + y)(3x - y)\), this is in the form of \((a+b)(a-b)\). Hence we apply the formula \(a^2 - b^2\) where \(a\) corresponds to \(3x\) and \(b\) corresponds to \(y\). So after applying the difference of squares formula we get \((3x)^2 - (y)^2.\)
02

Expand the expression

Then we expand the expression to get \(9x^2 - y^2\).

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Most popular questions from this chapter

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 \(-7^{0}\).

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)-(y-1)\left(y^{2}+y+1\right)$$

Perform the indicated operations. $$(y+6)^{2}-(y-2)^{2}$$

Discuss situations in which a vertical format, rather than a horizontal format, is useful for multiplying polynomials.
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