Simplifying and Expanding Quadratics - Algebra II

Cross multiply.

Set the equation equal to zero.

Factor to find the roots of the polynomial.

and

Use the FOIL method, which stands for First, Inner, Outer, Last:

To multiple these binomials, you can use the FOIL method to multiply each of the expressions individually.This will give you

or .

When multiplying this trinomial by this binomial, you'll need to use a modified form of FOIL, by which every term in the binomial gets multiplied by every term in the trinomial. One way to do this is to use the grid method.

You can also solve it piece-by-piece the way it is set up. First, multiply each of the three terms in the trinomail by . Then multiply each of those three terms again, this time by .

Finally, you can combine like terms after this multiplication to get your final simplified answer:

To add these two trinomials, you will first begin by combining like terms. You have two terms with , two terms with , and two terms with no variable. For the two fractions with , you can immediately add because they have common denominators:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses:

Next, identify and group the like terms in order to combine them: .

1. Cross multiply:

2. Set the equation equal to :

3. Factor to find the roots:

, so

, so

When given a quadratic in the form and told to solve by completing the square, we start by subtracting from both sides. In this problem is equal to , so we start by subtracting from both sides:

To complete the square we want to add a number to each side which yields a polynomial on the left side of the equation that can be simplified into a squared binomial . This number is equal to . In this problem is equal to , so:

We add to both sides of the equation:

We then factor the left side of the equation into binomial squared form and combine like terms on the right:

When given a quadratic in the form and told to solve by completing the square, we start by subtracting from both sides. In this problem is equal to , so we start by subtracting from both sides:

To complete the square we want to add a number to each side which yields a polynomial on the left side of the equals sign that can be simplified into a squared binomial . This number is equal to . In this problem is equal to , so:

We add to both sides of the equation:

We then factor the left side of the equation into binomial squared form and combine like terms on the right:

By foiling the binomials, multiplying the firsts, then the outers, followed by the inners and lastly the lasts, the expression you get is:

.

However, the expression can not be considered simplified in this state.

Distributing the two and adding like terms gives .

By factoring the equation you get . Values that are in both the numerator and denominator can be cancelled. Cancelling the values gives .

Factoring the expression gives . Values that are in both the numerator and denominator can be cancelled. By cancelling , the expression becomes .

Use the FOIL method to simplify the binomial.

Simplify the terms.

Notice that the coefficients can be aligned to the unknown variables. Solve for and .

The answer is:

Multiply each term of the first trinomial by second trinomial.

Add and combine like-terms.

The answer is:

The expression will need to be rearranged from highest to lowest powers in order to be simplified.

Factor a 2 in the numerator.

Factor the term in parentheses.

Factor the denominator.

Divide the numerator with the denominator.

The expression becomes:

The answer is:

The correct answer is or . The first step of the problem is to cross multiply. This will give the following equation:

After subtracting from each side the equation looks like:

The expression on the right hand side can be factored into:

Both and satisfy the above equation and are therefore the correct answers.