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Chapter 5: Problem 15

Add or subtract as indicated. $$\left(x^{3}+7 x y-5 y^{2}\right)-\left(6 x^{3}-x y+4 y^{2}\right)$$

Short Answer

Expert verified
The simplified expression is \( -5x^{3}+8xy-9y^{2} \)

Step by step solution

01

Distribute the negative sign

In the given problem, \( \left(x^{3}+7 x y-5 y^{2}\right)-\left(6 x^{3}-x y+4 y^{2}\right) \), subtracting involves changing the sign in front of the expression inside the second parentheses and then adding. When you distribute the negative sign, it switches the sign of every term inside the parentheses. So, the expression becomes - \( \left(x^{3}+7 x y-5 y^{2}\right) + \left(-6 x^{3}+x y-4 y^{2}\right) \)
02

Combine the like terms

Next, rewrite the expression by grouping the similar terms together. The similar terms are \( x^{3} \) from both sets of brackets and \( x y \) from both sets of brackets and \( y^{2} \) from both sets of brackets. So, the expression becomes \( x^{3}-6x^{3}+7xy+xy-5y^{2}-4y^{2} \)
03

Add/Subtract the like terms

Now, perform the addition and subtraction operations together for each type of like terms. So \( x^{3}-6x^{3}= -5x^{3} \), \( 7xy+xy= 8xy \), \( -5y^{2}-4y^{2}= -9y^{2} \).Thus, the simplified expression becomes \( -5x^{3}+8xy-9y^{2} \)

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Most popular questions from this chapter

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

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