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ACT Math : How to simplify binomials

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Example Questions

Example Question #1 : How To Simplify Binomials

Solve for x when 6x – 4 = 2x + 5

Possible Answers:

1/4

9/4

Correct answer:

9/4

Explanation:

Solve by simplifying:

6x – 4 = 2x + 5

6x = 2x + 9

4x = 9

x = 9/4

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Example Question #1 : How To Simplify Binomials

What is the value of the following equation if t = 3 and v = –4 ?

$\small 2t^2+4vt+2v^2$

Possible Answers:

Correct answer:

Explanation:

Substitute the numbers 3 and –4 for t and v, respectively.

$\small 2(3)^2+4(-4)(3)+2(-4)^2$

$\small 18+(-48)+32=2$

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Example Question #3 : How To Simplify Binomials

Simplify the following binomial:

$4x^2 + 16x - 4 - 2x^{2}$

Possible Answers:

x^2 + 8x - 2

2x^2 - 4x +16

x^2 - 4x +4

x^2 + 4x - 4

x^2 + 8x -4

Correct answer:

x^2 + 8x - 2

Explanation:

The equation that is presented is:

$4x^2 + 16x - 4 - 2x^{2}$

To get the correct answer, you first need to combine all of the like terms. So, you can subtract the 2x^2 from the 4x^2 , leaving you with:

2x^2 + 16x - 4

From there, you can reduce the numbers by their greatest common denominator, in this case, :

x^2 + 8x - 2

Then you have arrived at your final answer.

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Example Question #2 : How To Simplify Binomials

Simplify the following binomial expression:

16x^2 - 14x + 12x - 8 + 2

Possible Answers:

x^2 - 8x - 3

8x^2 + 2x -3

8x^2 - x - 3

4x^2 - 4x - 4

2x^2 - 4x - 3

Correct answer:

8x^2 - x - 3

Explanation:

First, combine all of the like terms that you are able:

16x^2 - 2x - 6

Then, reduce by the greatest common denominator (in this case, ):

8x^2 - x - 3

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Example Question #2 : How To Simplify Binomials

Simplify the following binomial:

$17x^{2} - 15x + 3x^{2 }+10x$

Possible Answers:

5x^2 - 3x

5(4x-x)

10x^2 - x

5x(4x-1)

5x^2(4x-x)

Correct answer:

5x(4x-1)

Explanation:

The equation presented in the problem is:

$17x^{2} - 15x + 3x^{2 }+10x$

First you have to combine the like terms, i.e. combining all instances of x^2 and :

20x^2 - 5x

Then, you can factor out the common to get your answer

5x(4x-1)

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ACT Math : How to simplify binomials

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Simplify Binomials

Example Question #1 : How To Simplify Binomials

Example Question #3 : How To Simplify Binomials

Example Question #2 : How To Simplify Binomials

Example Question #2 : How To Simplify Binomials

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