Add or subtract the polynomials.(2y2−9y+5)+(6y+4y2−7)(2y^2-9y+5)+(6y+4y^2-7)

6 y 2 − 3 y − 2 6y^2-3y-2 6 y 2 − 3 y − 2

Add or subtract the polynomials. ( 2 y 2 − 9 y + 5 ) + ( 6 y + 4 y 2 − 7 ) (2y^2-9y+5)+(6y+4y^2-7)

So now that we've done at least one practice problem together, go ahead and pause the video and try this one out on your own. We're gonna be doing a very similar thing here. We're gonna be adding or subtracting the following polynomials. We've got two y squared minus nine y plus five plus the second polynomial is six y plus four y squared minus seven. So we've got a plus, we're going to be adding these two polynomials which is good because we don't have to distribute a negative sign into the second one. Let's go ahead and identify our like terms and then start grouping them together. I've got a two y squared, so that's going to be one of the y squareds, and in the second polynomial I have a fair y squared. So, it's the same variable with the same exponent I can group those things together. What about the the next term? So, I've got a nine a minus nine y that's a single power of y, and in the second polynomial I've got a plus six y over here. That's also two terms I can group together. And then finally, I've got two constants. I've got a plus five and then a minus seven here. Now, again, because these two polynomials are added together, I can go ahead and just sort of drop the parentheses and start grouping those terms. So, I've got two y squared. I want to group it together the y squares. We've got a 2y squared plus, and then we've got a fair y squared over here, so I'm going to combine those things. Now, I've got a negative 9y, so remember I keep the sign that's in front, so negative nine y, and then we've got a plus six y over here. Again, this plus kind of just, it doesn't really affect any of the signs that are inside here, you keep all the signs the same. All right, so I've got a plus six y, and then finally what I've got is I've got a plus five minus a seven, so we've got the two blue terms together. So, now I can see I can sort of combine these things because they're a little bit closer together. We've got 2y and 4y. When you add these two things, you add the coefficients to a 6y and then we've got our terms in red which has got negative 9y plus 6y. So, now what we end up with is we actually end up with something that is negative here. So, this is going to be negative 3y and then for our final term, we've got plus five minus seven. The negative is larger, so we're going to end up with negative two over here. That's really all there is to it. We have one term of y squared, one of y, and one that's a constant. We can't simplify this any further. We've added these polynomials together. So, again, just go ahead and follow the rules for adding those things always add the like terms. I suggest color coding makes organizing these things much simpler. That's the final answer. Let me know if you have any questions. Thanks for watching. Hope you got the right answer.

Add or subtract the polynomials. ( 2 y 2 − 9 y + 5 ) + ( 6 y + 4 y 2 − 7 ) (2y^2-9y+5)+(6y+4y^2-7)

6 y 2 − 3 y − 2 6y^2-3y-2 6 y 2 − 3 y − 2

6 y 2 − 15 y − 2 6y^2-15y-2

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.
$(2 y^{2} - 9 y + 5) + (6 y + 4 y^{2} - 7)$

$6 y^{2} - 3 y + 2$

$6 y^{2} - 15 y - 2$

$6 y^{2} - 3 y + 12$

$6y^2-3y-2$

Verified step by step guidance

First, write down the two polynomials you need to add: $(2y^2 - 9y + 5)$ and $(6y + 4y^2 - 7)$.

Next, group like terms together. Like terms are terms that have the same variable raised to the same power. So, group the $y^2$ terms, the $y$ terms, and the constant terms separately: $(2y^2 + 4y^2) + (-9y + 6y) + (5 - 7)$.

Now, add the coefficients of each group of like terms. For the $y^2$ terms, add \$2$ and $4$. For the $y$ terms, add $-9$ and $6$. For the constants, add $5$ and $-7$.

After adding the coefficients, write the simplified polynomial by combining the results from each group: the sum of the $y^2$ terms, the sum of the $y$ terms, and the sum of the constants.

Finally, double-check your work to ensure all like terms were combined correctly and that the signs (positive or negative) were handled properly.

7:43m

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