All Algebra II Resources
Example Question #3 : How To Add Polynomials
Simplify x(4 – x) – x(3 – x).
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
Example Question #1 : Simplifying Expressions
Factor the numerator and denominator:
Cancel the factors that appear in both the numerator and the denominator:
Example Question #2 : Simplifying Expressions
and cancel out, leaving in the numerator. 5 and 25 cancel out, leaving 5 in the denominator
Example Question #3 : Simplifying Expressions
Simplify the following:
First, let us factor the numerator:
Example Question #7 : How To Multiply A Monomial By A Polynomial
Find the product:
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:
Example Question #4 : Simplifying Expressions
Multiply, expressing the product in simplest form:
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:
Example Question #5 : Simplifying Expressions
Simplify the following:
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:
Example Question #2 : How To Factor A Variable
Factor the expression:
To find the greatest common factor, we need to break each term into its prime factors:
Looking at which terms all three expressions have in common; thus, the GCF is . We then factor this out: .
Example Question #8 : How To Multiply A Monomial By A Polynomial
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.
Example Question #1 : How To Multiply Binomials With The Distributive Property
None of the other answers are correct.
First, distribute –5 through the parentheses by multiplying both terms by –5.
Then, combine the like-termed variables (–5x and –3x).