# Algebra 1 : How to subtract polynomials

## Example Questions

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### Example Question #1 : How To Subtract Polynomials

Subtract the polynomials below:

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:

Cannot be simplified further

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 #3 : Simplifying Polynomials

Rewrite the expression in simplest terms.

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 #5 : Solving Rational Expressions

Solve:

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 #1 : How To Subtract Polynomials

Simplify the following:

None of the other answers are correct.

Explanation:

First, FOIL the two binomials:

Then distribute the through the terms in parentheses:

Combine like terms:

### Example Question #12 : Simplifying Polynomials

Simplify.

Explanation:

Simplify

Distribute the negative:

Then combinde like terms

Subtract:

Explanation:

Subtract:

Explanation:

Subtract:

Explanation:

Subtract: