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

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 − 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 − 8 x 7x^3+7x^2+xy-8x

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

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21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 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

5. 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

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 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
33m

Quadratic Equations & Applications
41m

8. 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

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44m

9. Inequalities and Absolute Value2h 52m

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42m

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38m

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39m

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28m

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23m

10. Relations and Functions1h 10m

Introduction to Relations and Functions
25m

Function Notation
15m

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5m

Composition of Functions
24m

11. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

Simplifying Radical Expressions
27m

Adding and Subtracting Radicals
19m

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23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

12. Quadratic Equations and Functions1h 23m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
31m

13. Inverse, Exponential, & Logarithmic Functions1h 5m

Introduction to Inverse Functions
25m

Exponential Functions
13m

Introduction to Logarithmic Functions
26m

14. Conic Sections & Systems of Nonlinear Equations58m

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32m

Ellipses
15m

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10m

15. Sequences, Series, and the Binomial Theorem1h 20m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Factorials
11m

6. Exponents and Polynomials

Adding and Subtracting Polynomials

Beginning & Intermediate Algebra

6. Exponents and Polynomials

Adding and Subtracting Polynomials

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Multiple Choice

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

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

$7 x^{3} + 7 x^{2} + x y - 16$

$7 x^{3} + 7 x^{2} + x y - 14$

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

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Verified step by step guidance

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

Remove the parentheses since the operation between the polynomials is addition: \$7x^3 + xy - 8 + 7x^2 - 8$.

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

Add the coefficients of the like terms. For the constants, add $-8$ and $-8$ to combine them.

Write the simplified polynomial by combining all the terms after addition.

7:43m

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