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Chapter 5: Problem 14

Add or subtract as indicated. $$\left(6 x^{4} y^{2}-10 x^{2} y^{2}+7 x y\right)+\left(-12 x^{4} y^{2}-3 x^{2} y^{2}-x y\right)$$

Short Answer

Expert verified
The simplified expression is \(-6x^{4} y^{2} -13x^{2} y^{2} + 6x y\).

Step by step solution

01

Identify Like Terms

In the given expression, the like terms are: \(6x^{4} y^{2}\) and \(-12x^{4} y^{2}\), \(-10x^{2} y^{2}\) and \(-3x^{2} y^{2}\), \(7x y\) and \(-x y\).
02

Add or Subtract the Coefficients of Like Terms

Once the like terms have been identified, add or subtract the coefficients accordingly. So, from Step 1, we have: For the term \(x^{4} y^{2}\): \(6 -12 = -6\)For the term \(x^{2} y^{2}\): \(-10 -3 = -13\)For the term \(x y\): \(7 - 1 = 6\)Hence, the new coefficients for \(x^{4} y^{2}\), \(x^{2} y^{2}\) and \(x y\) are \(-6\), \(-13\) and \(6\) respectively.
03

Write Down the Final Result

Replace the coefficients for the like terms in the original expression to get the final result, as follows: \(-6x^{4} y^{2} -13x^{2} y^{2} + 6x y\).

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