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# Adding and subtracting polynomials

- Lesson: 1a1:27
- Lesson: 1b1:07
- Lesson: 1c1:25
- Lesson: 1d3:46
- Lesson: 2a0:38
- Lesson: 2b0:26
- Lesson: 2c0:22
- Lesson: 3a1:52
- Lesson: 3b1:18
- Lesson: 3c1:15
- Lesson: 3d1:29
- Lesson: 4a1:27
- Lesson: 4b0:55
- Lesson: 4c5:31
- Lesson: 4d1:08

## How to add and subtract polynomials

When adding and subtracting polynomials, youβll have to deal with combining like terms and also be aware of the order of operations within the question. A point youβll have to take note of before we begin so that you donβt make any mistakes is to be careful with minus signs.

What are like terms? Like terms are terms whose variables are the same. An example will be that 3x2 and 11x2 are like terms since their variables are both x2. However, 3x2 and 6x are not like terms, because one variable is x-squared whereas one is just x. You can see, however, that the coefficients do not have to be the same. In the first example just now, 3 and 11 are not the same, but they can still be combined because their variables are identical.

Letβs take a look at this example, which can demonstrate how adding and subtracting polynomials work. Weβll be carrying out basic operations with polynomials.

Question:

$\left( {x - 4xy - 2y} \right) + \left( {3xy - y} \right) + \left( { - 6x - 5y} \right)$

Solution:

$\left( {x - 4xy - 2y} \right) + \left( {3xy - y} \right) + \left( { - 6x - 5y} \right)$

1. Take out the parentheses

$x - 4xy - 2y + 3xy - y - 6x - 5y$

2. Look for like terms

$x - 4xy - 2y + 3xy - y - 6x - 5y$

3. Add and subtract.

$- 5x - 1xy - 7y$

Weβve outlined the three basic steps to solving a problem that deals with parentheses as well as both addition and subtraction. Letβs look more in depth into each of the steps.

In the first step, weβre removing the parentheses. This helps us identify the polynomials that weβll have to work with. Remember our note about paying attention to plus or minus signs? This is going to come in very handy soon. Since the signs outside the parentheses are both β+β, it makes removing the parentheses a lot easier.

Now that youβve got all your terms, itβs time to find the ones that are βlike termsβ. Weβve got a variety of variables, including βxβ, βxyβ, and βyβ. In step number 2, you can see how weβve put all the terms that have the same variables together to get ready to add polynomials or subtract polynomials. Always take the sign in front of your term with you when you move them around. Otherwise, youβll get the wrong answer, and may accidentally subtract when youβre supposed to add, or vice versa.

Working from left to right, start by adding polynomials, then subtracting polynomials in order. If there were powers in the variables, you would usually show your answer in order of descending powers. This means you may have to reorder your terms for your final answer.

In this example, we learned how to add and subtract polynomials horizontally. But similar to regular adding and subtracting, you can also do it vertically. For both methods, youβll end up with the same answer, so itβs mostly up to you whether you prefer to do it vertically or horizontally. You may find that for simple additions, using the horizontal method is easier since you wonβt have to rewrite the problem. However, as you progress into harder questions, the vertical method can help you ensure you donβt forget terms or minus signs.

For more examples, hereβs an interactive one that can give you through steps of polynomial addition/subtraction questions you type in. For a more in depth look at like terms, this is a link that will help.

##### Do better in math today

##### Don't just watch, practice makes perfect.

### Adding and subtracting polynomials

#### Lessons

- 1.Adding and Subtracting Polynomialsa)$\left( {4 - 2x + 3{x^2}} \right) + \left( { - x - 4{x^2} + 7} \right)$b)$\left( {7a + 1} \right) + \left( { - 4 - 3a} \right)$c)$\left( {{n^2} - 5} \right) + \left( {{n^2} + 6} \right)$d)$\left( x - 4xy - 2y \right) + \left( {3xy - y} \right) + \left( { - 6x - 5y} \right)$
- 2.Write the opposite of each expression.a)$- 2{x^3} + 5x - 4.6$b)$7n - 3$c)${y^2} - 8y + 1$
- 3.Subtract the following polynomials.a)$\left( { - 2{x^2} - 6x + 3} \right) - \left( {3{x^2} - x - 8} \right)$b)$\left( { - {x^2} + 7 - 3x} \right) - \left( {8 - x} \right)$c)$\left( {5{x^2} - 3x} \right) - \left( {2x - {x^2}} \right)$d)$\left( { - xy + 3x - 3} \right) - \left( { - x - 5 + 6xy} \right)$
- 4.Combine like terms.a)$\left( {{a^2} - 3a} \right) + \left( {2{a^2} - 4} \right) - \left( {6a - 1} \right)$b)$\left( {x + 5} \right) + \left( {2x - 3} \right) + \left( {7x - 6} \right)$c)$\left( { - 4x - 3.1} \right) - \left( { - 5.6x - 2} \right) - \left( {1.1x - 0.6} \right)$d)$\left( {3y - 2} \right) + \left( {y - 6} \right) + \left( {10y - 5} \right)$

##### Do better in math today

##### Don't just watch, practice makes perfect.

### Adding and subtracting polynomials

#### Don't just watch, practice makes perfect.

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