Algebra II : Simplifying and Expanding Quadratics

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #42 : Intermediate Single Variable Algebra

Solve the equation for .

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

Set the equation equal to zero.

Factor to find the roots of the polynomial.

 and

Example Question #1 : How To Use The Grid Method For Foil

Possible Answers:

Correct answer:

Explanation:

           

      

     

 

 

Example Question #1 : Quadratic Equations And Inequalities

Solve the equation for :

Possible Answers:

Correct answer:

Explanation:

 

1. Cross multiply:

 

2. Set the equation equal to :

 

3. Factor to find the roots:

,  so  

, so  

Example Question #1 : Simplifying And Expanding Quadratics

If you were to solve  by completing the square, which of the following equations in the form   do you get as a result?

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #2 : Simplifying And Expanding Quadratics

If you were to solve  by completing the square, which of the following equations in the form   do you get as a result?

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #1303 : Algebra Ii

Expand:

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

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

 

Example Question #3 : Simplifying And Expanding Quadratics

Multiply: 

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Simplifying And Expanding Quadratics

Multiply: 

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Subtract Trinomials

Subtract:

Possible Answers:

Correct answer:

Explanation:

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: .

Example Question #5 : Simplifying And Expanding Quadratics

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

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:

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