Simplifying Expressions - Algebra 2

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:

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!

In this form, the exponents are multiplied: .

In multiplication problems, the exponents are added.

In division problems, the exponents are subtracted.

It is important to know the difference.

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!

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:

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:

When multiplying exponential components, you must add the powers of each term together.

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:

Step 1: Find a common denominator for terms in numerator

Step 2: Divide

Simplify the first expression.

Rewrite the expression and combine like-terms.

The answer is:

Distribute the first term with the binomial.

Subtract the last term with this expression. Do not combine the terms as one unit. There are no like-terms, and the terms cannot simplified any further.

The answer is:

First, FOIL:

Simplify:

Distribute the through the parentheses:

Rewrite to make the expression look like one of the answer choices:

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

Now use the quotient rule on the variables by subtracting exponents:

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.

First, set up the division as the following:

Look at the leading term in the divisor and in the dividend. Divide by gives ; therefore, put on the top:

Then take that and multiply it by the divisor, , to get . Place that under the division sign:

Subtract the dividend by that same and place the result at the bottom. The new result is , which is the new dividend.

Now, is the new leading term of the dividend. Dividing by gives 5. Therefore, put 5 on top:

Multiply that 5 by the divisor and place the result, , at the bottom:

Perform the usual subtraction:

Therefore the answer is with a remainder of , or .

You must multiply out the first set of parenthesis (distribute) and you get 4x – x2. Then multiply out the second set and you get –3x + x2. Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x2 – x(3 – x)

4x – x2 – (3x – x2)

4x – x2 – 3x + x2 = x

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

When simplifying polynomials, only combine the variables with like terms.

can be added to , giving .

can be subtracted from to give .

Combine both of the terms into one expression to find the answer:

First, distribute –5 through the parentheses by multiplying both terms by –5.

Then, combine the like-termed variables (–5x and –3x).