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Algebra 1 : How to simplify binomials

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Example Questions

Example Question #1 : How To Simplify Binomials

Solve for :

3x +8 = 6x-4

Possible Answers:

x=4

$x=\frac{2}{3}$

x=-3

$x=\frac{4}{3}$

Correct answer:

x=4

Explanation:

In simplifying these two binomials, you need to isolate to one side of the equation. You can first add 4 from the right side to the left side:

3x +8 = 6x-4

3x +12 = 6x

Next you can subtract the from the left side to the right side:

12 = 3x

Finally you can divide each side by 3 to solve for :

4=x

You can double check this answer by plugging 4 into each binomial and confirm that they are equal to one another.

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Example Question #1 : How To Simplify Binomials

Solve for :

4z+10 = 6z-5

Possible Answers:

z=-2

z=7

$z=\frac{5}{2}$

$z=\frac{15}{2}$

Correct answer:

$z=\frac{15}{2}$

Explanation:

To simplify these two binomials, you need to isolate on one side of the equation. You first can add 5 from the right to the left side:

4z+10 = 6z-5

4z+15 = 6z

Next you can subtract from the left to the right side:

15 = 2z

Finally, you can isolate by dividing each side by 2:

$\frac{15}{2} = z$

You can verify this by plugging $\frac{15}{2}$ into each binomial to verify that they are equal to one another.

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Example Question #7 : Finding Roots

Solve for :

x^2+2 = 6x-6

Possible Answers:

x=1, 2

x=2,4

x=-2,-4

x=1,-2

Correct answer:

x=2,4

Explanation:

To solve for , you need to isolate it to one side of the equation. You can subtract the from the right to the left. Then you can add the 6 from the right to the left:

x^2+2 = 6x-6

x^2-6x+2 = -6

x^2-6x+8 = 0

Next, you can factor out this quadratic equation to solve for . You need to determine which factors of 8 add up to negative 6:

$(x \ \ \ \ \ \)(x \ \ \ \ \ \) = 0$

(x-2)(x-4)=0

Finally, you set each binomial equal to 0 and solve for :

$x=2 \ \ \ \ \ \ x=4$

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Example Question #1 : How To Simplify Binomials

Simplify:

(x-3)^2

Possible Answers:

x^2-6x+9

x^2+6x+9

x^2-9x+9x

x^2+9x+9

Correct answer:

x^2-6x+9

Explanation:

(a+b)^2=a^2+2ab+b^2

a=x

b=-3

x^2+2(-3)(x)+(-3)^2=x^2-6x+9

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Example Question #1 : How To Simplify Binomials

Solve for .

32x+37=43x-29

Possible Answers:

x=4

x=-6

x=6

x=-4

x=0

Correct answer:

x=6

Explanation:

32x + 37 = 43x – 29

Add 29 to both sides:

32x + 66 = 43x

Subtract 32x from both sides:

66 = 11x

Divide both sides by 11:

6 = x

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Example Question #5 : How To Simplify Binomials

Find in terms of :

7x-21y=56

Possible Answers:

$y=\frac{1}{3}x+\frac{8}{3}$

x=8-3y

$y=\frac{1}{3}x+\frac{8}{3}$

x=3y+8

x=3y-8

Correct answer:

x=3y+8

Explanation:

When solving for X in terms of Y, we simplify it so that Y is a variable that is used to represent the value of X:

7X-21Y=56

+21Y +21Y

7X=21Y+56

To find the value for X by itself, we then divide both sides by the coefficient of 7:

$\frac{7X}{7}=\frac{56}{7}+\frac{21Y}{7}$

Which gives the correct answer:

X=8+3Y

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Example Question #6 : How To Simplify Binomials

Simplify (8x^2+3x-5)-(-3.5x^2+x+3) .

Possible Answers:

11.5x^2+4x-8

11.5x^2+2x-2

4.5x^2+4x-2

11.5x^2+2x-8

4.5x^2+2x-2

Correct answer:

11.5x^2+2x-8

Explanation:

The question is asking for the simplified version of (8x^2+3x-5)-(-3.5x^2+x+3) .

Remember the distributive property of multiplication over addition and subtraction:

$ax^2+bx^2 = (a+b)x^2 \mathbf{AND}$ ax^2-bx^2 = (a-b)x^2

8x^2+3x-5+3.5x^2-x-3

Combine like terms.

8x^2+3.5x^2+3x-x-5-3

11.5x^2+2x-8

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Example Question #7 : How To Simplify Binomials

Which of the following is equivalent to the expression $x \cdot 2 + 7 ^{2}$ ?

Possible Answers:

2x+49

81x

None of the other answers yields a correct response

51x

$4x^{2}+ 28x+49$

Correct answer:

2x+49

Explanation:

Recall the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

$x \cdot 2 + 7 ^{2}$

$= x \cdot 2 + 49$

= 2x + 49

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Example Question #8 : How To Simplify Binomials

Which of the following is equivalent to the expression

$x + 2 \cdot 7 ^{2}$ ?

Possible Answers:

x+98

49x+98

x+196

$49x^{2} + 196x + 196$

$x^{2} + 28x + 196$

Correct answer:

x+98

Explanation:

Using the order of opperations, first simplify the exponent.

$x + 2 \cdot 7 ^{2}$

Next, perform the multiplication.

$= x + 2 \cdot 49$

= x + 98

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Algebra 1 : How to simplify binomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Simplify Binomials

Example Question #1 : How To Simplify Binomials

Example Question #7 : Finding Roots

Example Question #1 : How To Simplify Binomials

Example Question #1 : How To Simplify Binomials

Example Question #5 : How To Simplify Binomials

Example Question #6 : How To Simplify Binomials

Example Question #7 : How To Simplify Binomials

Example Question #8 : How To Simplify Binomials

All Algebra 1 Resources

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