Algebra II : Simplifying Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #51 : Simplifying Expressions

Simplify .

Possible Answers:

Correct answer:

Explanation:

To start, we can extract a  from both terms in the numerator to give:

Then we cancel the  terms:

Example Question #51 : Simplifying Expressions

Simplify .

Possible Answers:

Correct answer:

Explanation:

First we need to follow the order of operations, and do the multiplication first.  When you multiply like variables together, you add their exponents:

At this point we can no longer add the two remaining terms because their exponents are different, so we're done.

Example Question #53 : Simplifying Expressions

Simplify .

Possible Answers:

This cannot be simplified.

Correct answer:

Explanation:

When you multiply two terms with like variables you still multiply the constants together like normal.  In this case it would be:

The exponents would be added together for:

Putting the constant term in front, and the exponent back where it belongs, we have:

Example Question #54 : Simplifying Expressions

Use the distributive property of addition to simplify the following expression. (Do not factorize) .

Possible Answers:

Correct answer:

Explanation:

Use the distributive property to simplify the expression. The distributive property states that to multiply a sum by a term, you first multiply each part of the sum by that term separately, and then add these terms together. It looks like this in practice:

This means we multiply 5x by both terms, and then add these together.

Multiply the constant terms together, and the x's together to yield:

This expression is now simplified!

Example Question #55 : Simplifying Expressions

Simplify .

Possible Answers:

Correct answer:

Explanation:

When we multiply variables with exponents, we can break up the problem into two parts.  The first is what happens to the numbers in from of the variable, and the other is what happens to the numbers that are exponents for the variable.

First, let's start with the numbers in front of the variable.  To figure this out, we simply multiply the two numbers together, like normal:

Next, let's take a look at the exponents. To figure out the exponents, we would add the two numbers together (remember you can only do this if you're multiplying/dividing; you can't add two variables unless their exponents are the same):

Now we just put the answer for the number in front of the variable and the answer for the exponents back where we found them: 

Example Question #56 : Simplifying Expressions

Simplify .

Possible Answers:

Correct answer:

Explanation:

It would be easier to first expand the function to see what we're working with:

Here we can see that the  will simplify into , and that the two 's in the denominator will cancel with two of the 's in the numerator.  That leaves us with:

When we collect the terms together we end up with:

Example Question #57 : Simplifying Expressions

Simplify the following expression:

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Since this is a cubed-root of terms that are multiplied together, it can be thought of as taking the cubed-root of each of the following terms -- or "how many groups of 3 are there"

: There is no cubed-root of 6, so it stays inside the root -- 

: there is 1 group of 3 in 4 with 1 left over. So one  goes outside to represent the 1 group of 3, and the "left over"  stays inside the root -- 

: there are 3 groups of 3 in 9 with none leftover. So,  goes outside to represent the 3 groups of 3, and there is nothing left inside -- 

: there are 4 groups of 3 in 14 with 2 left over. So,  goes outside to represent the 4 groups of 3, and the "left over"  stays inside the root -- 

 

Combining like terms: 

Example Question #58 : Simplifying Expressions

Use the distributive property to expand the expression.

Possible Answers:

Correct answer:

Explanation:

Use the distributive property to simplify the expression. The distributive property states that to multiply a sum by a term, you first multiply each part of the sum by that term separately, and then add these terms together. It looks like this in practice:

This means we multiply -6x2 by both terms, and then add these together. Don't forget, the negative sign gets applied to each term within the sum.

Multiply the constant terms together, and the x's together to yield:

This expression is now simplified!

Example Question #59 : Simplifying Expressions

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Step 1: A power raised to a power can be simplified by multiplying the two powers.

Step 2: When a fraction is raised to a power, it applies to both the top and bottom. Again, you multiply the powers.

Step 3: When dividing exponents with the same base, you subtract the power of the bottom from the power of the top.

 

Example Question #60 : Simplifying Expressions

Simplify the expression:  

Possible Answers:

Correct answer:

Explanation:

Simplify the first expression.

Rewrite the expression and combine like-terms.

The answer is:  

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