Multiplying Trinomials and Polynomials

When multiplying trinomials or polynomials, you just distribute all of the terms in the first polynomial. Basically, this is the same as multiplying binomials except you cannot use the shortcut FOIL.

Examples:

1)





First, we distribute the and get

Next, we distribute the 3 and get

Now we have , but we are not finished because there is a set of like terms that we can add together. Add 4x2 and 3x2to get 7x2. Also add 1x and 12x to get 13x. Make sure the final answer is in standard form:.

2)





First, we distribute the and get

Next, we distribute theand get

Then, we distribute theand get

Now we have , but we are not finished because we can combine like terms. Combine them to get our final answer (in standard form): .


As you can see, it doesn't matter how many terms are in each polynomial. You just keep distributing. It's not hard, but you do have to be very careful in your work.

Practice:: Multiply the polynomials

1)

2)

3)

4)

5)

Answers: 1) x3 + 13x2 + 38x - 16 2) y3 + 6y2 - 15y - 2 3) x4 + x3 -3x 2 + 4x + 2 4) y4 - 3y3 -2y 2 + 2y + 12 5) x4 + 3x3 + 5x2 - 2x - 5

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Math
Algebra
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