Problem 18 Add or subtract as indicated. ... [FREE SOLUTION]

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Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 5: Problem 18

Add or subtract as indicated. $$\left(5 x^{4} y^{2}+6 x^{3} y-7 y\right)-\left(3 x^{4} y^{2}-5 x^{3} y-6 y+8 x\right)$$

Short Answer

Expert verified

The result of the operation is $2 x^{4} y^{2} + 11 x^{3} y - y - 8 x$

Step by step solution

Distribute the Subtraction

We first distribute the subtraction operator across the polynomial that's immediately after it. In essence, we change the sign of each term in the second parentheses: $3 x^{4} y^{2}$, $-5 x^{3} y$, $-6 y$ and $8 x$. We thus get: $5 x^{4} y^{2} + 6 x^{3} y - 7 y - 3 x^{4} y^{2} + 5 x^{3} y + 6 y - 8 x$.

Combine Like Terms

We then combine the like terms. Each term in a polynomial consists of a product of variables or constants. Like terms have the same combination of variables, although these can be multiplied by different constants. Here, the like terms are: $5 x^{4} y^{2}$ and $-3 x^{4} y^{2}$, $6 x^{3} y$ and $5 x^{3} y$, and $-7 y$ and $6 y$. The term $-8 x$ does not combine with any other term. That gives us: $(5 x^{4} y^{2} - 3 x^{4} y^{2}) + (6 x^{3} y + 5 x^{3} y) + (-7 y + 6 y) - 8 x$

Solve

Finally, we simplify the expression by carrying out the addition and subtraction. This gives us: $2 x^{4} y^{2} + 11 x^{3} y - y - 8 x$

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91影视

Add or subtract as indicated. $$\left(5 x^{4} y^{2}+6 x^{3} y-7 y\right)-\left(3 x^{4} y^{2}-5 x^{3} y-6 y+8 x\right)$$

Short Answer

Step by step solution

Distribute the Subtraction

Combine Like Terms

Solve

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