Add or subtract the polynomials.(7x3+xy−8)+(7x2−8)(7x^3+xy-8)+(7x^2-8)

7 x 3 + 7 x 2 + x y − 16 7x^3+7x^2+xy-16 7 x 3 + 7 x 2 + x y − 16

Add or subtract the polynomials. ( 7 x 3 + x y − 8 ) + ( 7 x 2 − 8 ) (7x^3+xy-8)+(7x^2-8)

So, let's get started with this practice problem here. We're going to add these two polynomials together. We've got seven x cubed plus x y minus eight plus seven x squared minus eight as our second polynomial. Again, we're going to go ahead and just see, we can color code, different terms that are similar to each other so we can combine them. We're going to be adding these two polynomials so we don't have to distribute a minus sign into any parentheses. Let's get started here. Alright, we've got a seven x cubed. Is there any other term in any of the polynomials that has an x and also a cubed? Remember, it has to be the same variable and same exponent. Well, there's actually nothing else over here, so we're done. What about x y? So, we've got an x y over here, nothing else in either the polynomials or the remaining terms has x y in it. Here we have a minus eight which is a constant, but we also notice that the second polynomial also has a minus eight. And then finally, for the last term, the only other term that remains, we have a seven x squared. You might think to combine it with the seven x cubed, but remember it has to be the same variable and also the same exponent. You can't combine the seven x squared with the seven x cubed because they're not like terms. Alright, so I'm just going to give this another color over here. So, there's really not a whole lot we can actually combine, and this is going to happen sometimes in your problems. The answer is pretty straightforward. The seven x squared just or sorry, seven x cubed just remains seven x cubed plus the x y, and then what happens is the minus eight can combine with the minus eight. But typically, we just write constants on the end. So, I'm just going to save this for the end. We're going to write the seven x squared over here, and then now we can go ahead and combine these like terms. So, if I combine a negative eight added to another negative eight, what do I get? It doesn't cancel out because we're combining a negative and a negative this becomes negative 16. Alright, and that's our final answer. We can't simplify anything further because we can't combine any more like terms. That's all there is to it. Let me know if you have any questions. Let's keep going.

Add or subtract the polynomials. ( 7 x 3 + x y − 8 ) + ( 7 x 2 − 8 ) (7x^3+xy-8)+(7x^2-8)

7 x 3 + 7 x 2 + x y − 16 7x^3+7x^2+xy-16 7 x 3 + 7 x 2 + x y − 16

7 x 3 + 7 x 2 + x y − 8 7x^3+7x^2+xy-8

7 x 3 + 7 x 2 + x y − 14 7x^3+7x^2+xy-14 7 x 3 + 7 x 2 + x y − 14

7 x 3 + 7 x 2 + x y − 8 x 7x^3+7x^2+xy-8x 7 x 3 + 7 x 2 + x y − 8 x

6. Exponents, Polynomials, and Polynomial Functions

Adding and Subtracting Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Adding and Subtracting Polynomials

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Multiple Choice

Add or subtract the polynomials.
$(7 x^{3} + x y - 8) + (7 x^{2} - 8)$

$7 x^{3} + 7 x^{2} + x y - 8$

$7x^3+7x^2+xy-16$

$7x^3+7x^2+xy-14$

$7x^3+7x^2+xy-8x$

Verified step by step guidance

Identify the two polynomials to be added: $\left(7x^{3} + xy - 8\right)$ and $\left(7x^{2} - 8\right)$.

Remove the parentheses since the operation between the polynomials is addition, so the signs of the terms remain the same.

Group like terms together. Like terms have the same variables raised to the same powers. Here, group \$7x^{3}$, $7x^{2}$, $xy$, and the constants $-8$ and $-8$.

Add the coefficients of the like terms: \$7x^{3}$ stays as is, $7x^{2}$ stays as is, $xy$ stays as is, and add the constants $-8 + (-8)$.

Write the simplified polynomial by combining the results from the previous step, keeping the terms in standard form (usually descending powers of $x$).

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