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Algebra 1 : Binomials

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Example Questions

Example Question #1 : How To Simplify Binomials

Solve for :

3x +8 = 6x-4

Possible Answers:

x=4

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

x=-3

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

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=7

z=-2

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

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

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 #5 : Finding Roots

Solve for :

x^2+2 = 6x-6

Possible Answers:

x=2,4

x=-2,-4

x=1,-2

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 : Foil

Simplify:

(x-3)^2

Possible Answers:

x^2-9x+9x

x^2+9x+9

x^2-6x+9

x^2+6x+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=-6

x=6

x=4

x=0

x=-4

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 #4 : How To Simplify Binomials

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

Possible Answers:

4.5x^2+2x-2

11.5x^2+2x-2

11.5x^2+4x-8

4.5x^2+4x-2

11.5x^2+2x-8

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 #281 : Variables

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

Possible Answers:

None of the other answers yields a correct response

2x+49

81x

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 #4 : How To Simplify Binomials

Which of the following is equivalent to the expression

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

Possible Answers:

x+98

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

49x+98

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

x+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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Example Question #1 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{2}$ in the product

$\left ( x+ 0.4\right ) (x - 0.2) (3x-0.7)$ .

Possible Answers:

0.7

1.3

2.5

-0.1

0.5

Correct answer:

-0.1

Explanation:

While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two terms and one constant are multiplied; find the three products and add them, as follows:

$\left (\underline{ x}+ 0.4\right ) (\underline{x} - 0.2) (3x\underline{-0.7})$

$x \cdot x \cdot (-0.7) = -0.7x^{2}$

$\left (\underline{ x}+ 0.4\right ) (x \underline{-0.2})(\underline{3x}-0.7)$

$x \cdot (-0.2) \cdot 3x= -0.6x^{2}$

$\left (x+ \underline{0.4}\right ) (\underline{x} - 0.2)(\underline{3x}-0.7)$

$0.4 \cdot x \cdot 3x = 1.2 x^{2}$

Add: $-0.7x^{2}+ (-0.6x^{2})+ 1.2x^{2} = -0.1x^{2}$ .

The correct response is -0.1 .

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Algebra 1 : 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 #5 : Finding Roots

Example Question #1 : Foil

Example Question #1 : How To Simplify Binomials

Example Question #5 : How To Simplify Binomials

Example Question #4 : How To Simplify Binomials

Example Question #281 : Variables

Example Question #4 : How To Simplify Binomials

Example Question #1 : How To Find The Value Of The Coefficient

All Algebra 1 Resources

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