Simplifying Expressions - Algebra II

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

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:

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).

First, mulitply the mononomial by the first term of the polynomial:

Second, multiply the monomial by the second term of the polynomial:

Add the terms together:

First we will foil the first function before distributing.

We will then distribute out the

We will then distribute out the

Now the only like terms we have are and , so our final answer is:

. However, cannot be simplified any further because the terms have different exponents.

(Like terms are terms that have the same variables with the same exponents. Only like terms can be combined together.)

times gives us , while times 4 gives us . So it equals .

and cancel out, leaving in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

distributes to , multiplying to become , and distributes to , multiplying to make .

Be sure to distribute the along with its coefficient.

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

First, FOIL the two binomials:

Then distribute the through the terms in parentheses:

Combine like terms:

First we will factor the numerator:

Then factor the denominator:

We can re-write the original fraction with these factors and then cancel an (x-5) term from both parts:

First, let us factor the numerator: