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Pre-Algebra : Adding and Subtracting Polynomials

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Example Questions

Example Question #11 : Polynomials

Simplify the following expression:

8x + 6 - 2x + 2

Possible Answers:

6x^2 + 8

6x + 8

8x + 6

16-2x

Correct answer:

6x + 8

Explanation:

The simplify this expression, combine like terms. Terms are like if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.

and -2x are like terms (both have the variable ). To combine them, you do 8x - 2x = 6x

6 and 2 are also like terms (both have no variable). To combine them, you do 6 + 2 = 8 .

You now have your simplified expression: 6x + 8 which is the final answer.

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Example Question #12 : Polynomials

If $\small \small X= 3a^3 +2a^2 +a$ and $\small Y= 9a^4 +3a +1$ , what is $\small X+Y$ ?

Possible Answers:

$\small 9a^4 +3a^3+2a^2+4a+1$

$\small \small 9a^4 +3a^3+2a^2+3a+1$

$\small 12a^4 + 2a^2 + 4a +1$

$\small 12a^{3} + 3a^3 +a +1$

$\small 9a^4 + 6a^3 + 2a^2 +a +1$

Correct answer:

$\small 9a^4 +3a^3+2a^2+4a+1$

Explanation:

The first step is to write out $\small X+Y$ as

$\small X+ Y= (3a^3 +2a^2 +a) + (9a^4 +3a +1)$

The next step is to re-arrange the expression so it is ordered by exponential degree, as:

$\small X+ Y= (9a^4 +3a^3 +2a^2 +a+3a +1)$

The final step is to sum together like terms and simplify the expression, as follows:

$\small \small \small X+ Y= (9a^4 +3a^3 +2a^2 +(a+3a) +1) = (9a^4 +3a^3 +2a^2 +4a +1)$

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Example Question #13 : Polynomials

Simplify.

$5x^{3}+6x-3 - \left ( 3x-2x^{2} +1 \right )$

Possible Answers:

$5x^{3}-2x^{2}+3x-2$

$7x^{3}-5x^{2}+3x+1$

$5x^{3}+2x^{2}+9x-4$

$5x^{3}+2x^{2}+3x-4$

Correct answer:

$5x^{3}+2x^{2}+3x-4$

Explanation:

First distribute the negative:

$5x^{3}+6x-3+ \left ( -3x+2x^{2}-1 \right )$

Group like terms, meaning terms that have the same variable and same exponent:

$5x^{3}+2x^{2}+6x- 3x-3 -1$

Add the like terms:

$5x^{3}+2x^{2}+3x-4$

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Example Question #14 : Polynomials

Simplify:

$x^{4}+3x^{2}+14x-(x^4-3x^3+2x^2)$

Possible Answers:

3x^3+x^2+14x

-2x^4+3x^3+x^2+14x

3x^3+x^2-14x

2x^3+x^2+14x

2x^4+3x^3+x^2+14x

Correct answer:

3x^3+x^2+14x

Explanation:

To solve you must first distribute the negative to the parentheses

x^4+3x^2+14x-x^4+3x^3-2x^2

Then you should combine like terms and you are left with

3x^3+x^2+14x

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Example Question #15 : Polynomials

Simplify: (2x^2 + x) + (x^2 -3x + 1)

Possible Answers:

2x^3 - x^2

2x^2 + 4x + 1

2x^4 -3x + 1

2x^2 -2x + 1

3x^2 -2x+1

Correct answer:

3x^2 -2x+1

Explanation:

To simplify, we will combine like terms.

(2x^2 + x) + (x^2 -3x + 1) This has two terms with x^2 , and two terms with , so we will group those together:

2x^2 + x^2 + x - 3x + 1 Now we can add together the like terms. Remember that if a term doesn't have a coefficient [number in front of it], there is only one of them:

3x^2 -2x + 1

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Example Question #16 : Polynomials

Simplify the following expression:

(4x+7y)-(2x-5y)

Possible Answers:

=2x+2y

=2x+12y

=6x+12y

=11x+3y

=4(x+y)

Correct answer:

=2x+12y

Explanation:

Combine the like terms (x's together and y's together).

Don't forget to distribute the negative sign through the parenthesis.

(4x+7y)-(2x-5y)

=4x+7y-2x+5y

=4x-2x+7y+5y

=2x+2y

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Example Question #17 : Polynomials

Subtract these polynomials: (4x^4-2x^3+x+8)-(2x^5-2x^4+3x+1)

Possible Answers:

2x^5+6x^4-2x^3-2x-7

-2x^5+6x^4-2x^3-2x+7

-2x^5+2x^4-2x^3-2x+7

Answer is not present.

-2x^5+6x^4-2x^3+4x+7

Correct answer:

-2x^5+6x^4-2x^3-2x+7

Explanation:

Distribute appropriate sign and simplify:

(4x^4-2x^3+x+8)-(2x^5-2x^4+3x+1)

${\color{Green} 4x^4}-2x^3+x+8-2x^5+{\color{Green} 2x^4}-3x-1$

${\color{Green} 6x^4}-2x^3+{\color{Red} x}+8-2x^5-{\color{Red} 3x}-1$

${\color{Green} 6x^4}-2x^3-{\color{Red} 2x}+{\color{Blue} 8}-2x^5-{\color{Blue} 1}$

${\color{Green} 6x^4}-2x^3+{\color{Red} 2x}+{\color{Blue} 7}-2x^5$

Rearrange into standard form(descending degree or powers):

-2x^5+6x^4-2x^3-2x+7

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Example Question #18 : Adding And Subtracting Polynomials

Add the following polynomials:

(3x + 7y - 5z) + (-2x - 6y + 4z) =

Possible Answers:

x + y + 9z

x + y - z

5x + 13y + 9z

x + 13y + z

x + y + z

Correct answer:

x + y - z

Explanation:

(3x + 7y - 5z) + (- 2x - 6y + 4z) =

3x + 7y - 5z + - 2x - 6y + 4z =

(3x - 2x) (7y - 6y) (-5z + 4z) =

x + y - z

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Example Question #12 : Adding And Subtracting Polynomials

Simplify the expression.

$3a^{2} + 10a^{2} - 5b^{2}$

Possible Answers:

$13a^{4}- 5b^{2 }$

$8ab^{2}$

$13a^{2} - 5b^{2}$

$8ab^{2}$

Correct answer:

$13a^{2} - 5b^{2}$

Explanation:

When adding or subtracting polynomials with exponents, the value of the exponent never changes. The exponent does change when multiplying or dividing.

Start by categorizing each polynomial into groups according to the variable, then according to the like variable's exponent. Because $3a^{2}$ and $10a^{2}$ share a common variable AND exponent, you may add the coefficients:

$3a^{2} + 10 a^{2} = 13a^{2 }$

However, because $5b^{2}$ does not share the same variable, you may not subtract it from $13a^{2 }$ . Therefore, you leave the rest as is:

$13a^{2} - 5b^{2}$

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Example Question #18 : Polynomials

Solve: -(x^2+3x)-(x^2-3x)

Possible Answers:

-2x^2+6x

-2x^2

-2x^2-6x

Correct answer:

-2x^2

Explanation:

To simplify this expression, it is necessary to eliminate the parentheses grouping the terms. Distribute the negative signs. Double negative translate the sign to a positive.

-(x^2+3x)-(x^2-3x) = -x^2-3x - x^2+3x

The answer is -2x^2 .

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Pre-Algebra : Adding and Subtracting Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Polynomials

Example Question #12 : Polynomials

Example Question #13 : Polynomials

Example Question #14 : Polynomials

Example Question #15 : Polynomials

Example Question #16 : Polynomials

Example Question #17 : Polynomials

Example Question #18 : Adding And Subtracting Polynomials

Example Question #12 : Adding And Subtracting Polynomials

Example Question #18 : Polynomials

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