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.

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1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving Coming soon

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics Coming soon

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement Coming soon

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

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26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

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35m

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41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

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27m

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26m

Factorials
11m

13. Exponents and Polynomials

Adding and Subtracting Polynomials

Prealgebra, Beginning Algebra, & Intermediate Algebra

13. Exponents and Polynomials

Adding and Subtracting Polynomials

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Multiple Choice

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

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

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

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

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

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

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