How to subtract polynomials - Algebra 1

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:

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.

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:

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:

Sum the first two expressions:

Subtract the sum from to get:

By combining like terms we get:

Simplify

Distribute the negative:

Then combinde like terms

Answer:

First, we will need to distribute the minus sign.

Then, combine like terms.

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:

We subtract polynomials just like we would anything else, but we must pay attention to the sign after using the distributive property on the sign that separates the two polynomials in subtraction problems. Then, of course, only like terms can combine or subtract from each other.

Start by distributing the negative sign into the second polynomial:

Now combine or subtract like terms based on the sign between them (same colored terms cancel each other out):

Left over:

Use distribution to simplify the signs of the polynomials.

Combine like terms while following coefficient rules.

The correct expanded and simplified answer will be

.

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):