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Chapter 5: Problem 79

Use a vertical format to subtract the polynomials. $$\begin{array}{r} 9 y^{2}-6 \\ -\left(-5 y^{2}+2\right) \\ \hline \end{array}$$

Short Answer

Expert verified
The subtraction of the polynomials is \(14y^2 - 8\).

Step by step solution

01

Rewrite the subtraction as an addition

Given the polynomials \(9y^2 - 6\) and \(-5y^2 + 2\). The operation is a subtraction, but we are subtracting a negative, which is the same as adding a positive. So your new operation would look like this: \(9y^2 - 6 + 5y^2 - 2\).
02

Simplify and combine like terms

Now that we have the polynomials written as an addition, we can combine like terms. Combining \((9y^2 + 5y^2)\) and \((-6 - 2)\), we get \(14y^2 - 8\).
03

Formulate the final answer

The final subtraction of the two polynomials is then \(14y^2 - 8\). This is our final answer.

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Most popular questions from this chapter

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

In Exercises \(79-82,\) simplify each expression. $$\left(\frac{18 x^{2} y^{4}}{9 x y^{2}}\right)-\left(\frac{15 x^{5} y^{6}}{5 x^{4} y^{4}}\right)$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$534.7=5.347 \times 10^{3}$$

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

In Exercises \(79-82,\) simplify each expression. Divide the sum of \((y+5)^{2}\) and \((y+5)(y-5)\) by \(2 y\)
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