Algebra 1 : How to simplify binomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Simplify Binomials

Solve for :

Possible Answers:

Correct answer:

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:

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

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

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

Example Question #2 : How To Simplify Binomials

Solve for :

Possible Answers:

Correct answer:

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:

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

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

You can verify this by plugging  into each binomial to verify that they are equal to one another.

Example Question #1 : Solving Equations

Solve for :

Possible Answers:

Correct answer:

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:

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

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

Example Question #3 : How To Simplify Binomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : How To Simplify Binomials

Solve for .

Possible Answers:

Correct answer:

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

Example Question #4 : How To Simplify Binomials

 

 

Find  in terms of :

Possible Answers:

Correct answer:

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:

               

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

Which gives the correct answer:

Example Question #6 : How To Simplify Binomials

Simplify .

Possible Answers:

Correct answer:

Explanation:

The question is asking for the simplified version of .

Remember the distributive property of multiplication over addition and subtraction:

 

 

Combine like terms.

Example Question #7 : How To Simplify Binomials

Which of the following is equivalent to the expression  ?

Possible Answers:

None of the other answers yields a correct response

Correct answer:

Explanation:

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

Example Question #8 : How To Simplify Binomials

Which of the following is equivalent to the expression

 ?

Possible Answers:

Correct answer:

Explanation:

Using the order of opperations, first simplify the exponent.

Next, perform the multiplication.

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