Chapter 5: Q. 5.15 (page 492)

$Simplify: (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2})$

Short Answer

Expert verified

The simplified form of the given expression is $x^{3} - y^{3}$ .

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenpolynomialexpressionis \\ (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2}) \\ Wehavetosimplifythegivenexpression. \end{array}$

Step 2. Distribute and identify like terms

$\begin{array}{l} Wehave (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2}) \\ Distribute \\ \Rightarrow (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2}) = x^{3} - x^{2} y - x y^{2} - y^{3} + x^{2} y + x y^{2} \\ Identifyliketerms \\ = x^{3} - \underline{x^{2} y} - \underline{\underline{x y^{2}}} - y^{3} + \underline{x^{2} y} + \underline{\underline{x y^{2}}} \\ Rearrangetheterms \\ = x^{3} - y^{3} - \underline{x^{2} y} + \underline{x^{2} y} - \underline{\underline{x y^{2}}} + \underline{\underline{x y^{2}}} \\ = x^{3} - y^{3} \end{array}$

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$Simplify: (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Distribute and identify like terms

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Simplify:x3-x2y-xy2+y3+x2y+xy2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Distribute and identify like terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

$Simplify: (x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2})$