Algebra 1 : How to subtract polynomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #110 : Polynomials

Subtract the polynomials below:

Possible Answers:

Correct answer:

Explanation:

The first step is to get everything out of parentheses to combine like terms. Since the polynomials are being subtracted, the sign of everything in the second polynomial will be flipped. You can think of this as a  being distributed across the polynomial:

Now combine like terms:

Example Question #1 : How To Subtract Polynomials

Simplify the expression: 

Possible Answers:

Cannot be simplified further

Correct answer:

Explanation:

Don't be scared by complex terms! First, check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was .

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match! So we just subtract the coefficients of the matching terms and we get our answer:

Example Question #2 : How To Subtract Polynomials

Rewrite the expression in simplest terms.

Possible Answers:

 

Correct answer:

Explanation:

In simplifying this expression, be mindful of the order of operations (parenthical, division/multiplication, addition/subtraction).  

Since operations invlovling parentheses occur first, distribute the factors into the parenthetical binomials. Note that the  outside the first parenthetical binomial is treated as  since the parenthetical has a negative (minus) sign in front of it. Similarly, multiply the members of the expression in the second parenthetical by  because of the negative (minus) sign in front of it. Distributing these factors results in the following polynomial.

Now like terms can be added and subtracted. Arranging the members of the polynomial into groups of like terms can help with this. Be sure to retain any negative signs when rearranging the terms.

Adding and subtracting these terms results in the simplified expression below.

Example Question #4 : Solving Rational Expressions

Solve:

 

 

Possible Answers:

Correct answer:

Explanation:

First we convert each of the denominators into an LCD which gives us the following:

Now we add or subtract the numerators which gives us:

 

Simplifying the above equation gives us the answer which is:

Example Question #13 : Simplifying Expressions

Simplify the following:

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

First, FOIL the two binomials:

Then distribute the through the terms in parentheses:

Combine like terms:

Example Question #3 : How To Subtract Polynomials

Simplify the following expression.

Possible Answers:

Correct answer:

Explanation:

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms together:

has no like terms.

Combine these terms into one expression to find the answer:

Example Question #6 : How To Subtract Polynomials

Simplify.

Possible Answers:

Correct answer:

Explanation:

Simplify

Distribute the negative: 

Then combinde like terms

Answer: 

Example Question #16 : Simplifying Polynomials

Subtract:

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : How To Subtract Polynomials

Subtract:

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : How To Subtract Polynomials

Subtract:

Possible Answers:

Correct answer:

Explanation:

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