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Chapter 5: Problem 20

Add or subtract as indicated. $$\left(x^{3}-y^{3}\right)-\left(-6 x^{3}+x^{2} y-x y^{2}+2 y^{3}\right)$$

Short Answer

Expert verified
The simplified expression is \(7x^{3}-x^{2}y+xy^{2}-3y^{3}\)

Step by step solution

01

Distribute the Negative Sign

Subtracting a polynomial is like adding its opposite. You need to distribute the negative through the parentheses to each terms- which will change the signs of each of the terms inside the parentheses. So, \[ \left(x^{3}-y^{3}\right)-\left(-6x^{3}+x^{2}y-xy^{2}+2y^{3}\right) \] becomes \[ x^{3}-y^{3}+6x^{3}-x^{2}y+xy^{2}-2y^{3} \]
02

Combine like terms

Like terms are terms with the same variable and power. After the distribution, the polynomial contains like terms that can be combined. In this case, the like terms are \(x^{3}\) and \(6x^{3}\), and \(-y^{3}\)and \(-2y^{3}\). Combine those like terms together, which results in \[ 7x^{3}-x^{2}y+xy^{2}-3y^{3} \]

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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.

Explain how to find any nonzero number to the 0 power.

Use a vertical format to find each product. $$\begin{array}{l}x^{2}+7 x-3 \\\x^{2}-x-1 \\\\\hline\end{array}$$

Perform the indicated operations. $$(x+4)(x-5)-(x+3)(x-6)$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x-3)\) b. \((x+5)(x-5)\)
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