Question

expressions-polynomials-evaluate / polynomials: problem 8 (1 point) add or subtract the given polynomials as indicated \\(\

$$\begin{array}{r}9a^{5}b^{7} + 10a^{4}b^{2} + 10ab \\\\ -(2a^{5}b^{7} - 4a^{4}b^{2} + 7ab) \\\\ \\hline 7a^{5}b^{7}+14a^{4}b^{2}+7ab\\end{array}$$

\\)

Explanation:

Step1: Distribute the negative sign

We have to distribute the negative sign to each term inside the parentheses: $-(2a^{5}b^{7}-4a^{4}b^{2}+7ab)= -2a^{5}b^{7}+4a^{4}b^{2}-7ab$

Step2: Combine like terms for $a^{5}b^{7}$ terms

The terms with $a^{5}b^{7}$ are $9a^{5}b^{7}$ and $-2a^{5}b^{7}$. Combining them: $9a^{5}b^{7}-2a^{5}b^{7}=7a^{5}b^{7}$

Step3: Combine like terms for $a^{4}b^{2}$ terms

The terms with $a^{4}b^{2}$ are $10a^{4}b^{2}$ and $4a^{4}b^{2}$. Combining them: $10a^{4}b^{2}+4a^{4}b^{2}=14a^{4}b^{2}$

Step4: Combine like terms for $ab$ terms

The terms with $ab$ are $10ab$ and $-7ab$. Combining them: $10ab - 7ab=3ab$

Wait, there was a mistake in the initial calculation. Let's redo the $ab$ term calculation.

Step1 (revised): Distribute the negative sign

$-(2a^{5}b^{7}-4a^{4}b^{2}+7ab)= -2a^{5}b^{7}+4a^{4}b^{2}-7ab$

Step2 (revised): Combine $a^{5}b^{7}$ terms

$9a^{5}b^{7}-2a^{5}b^{7}=7a^{5}b^{7}$

Step3 (revised): Combine $a^{4}b^{2}$ terms

$10a^{4}b^{2}+4a^{4}b^{2}=14a^{4}b^{2}$

Step4 (revised): Combine $ab$ terms

$10ab-7ab = 3ab$

So the correct result should be $7a^{5}b^{7}+14a^{4}b^{2}+3ab$

Answer:

$7a^{5}b^{7}+14a^{4}b^{2}+3ab$