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) $Multiplying trinomials and polynomials img 1$

$Multiplying trinomials and polynomials img 2$

$Multiplying trinomials and polynomials img 3$

First, we distribute the $Multiplying trinomials and polynomials img 4$ and get $Multiplying trinomials and polynomials img 5$

Next, we distribute the 3 and get $Multiplying trinomials and polynomials img 6$

Now we have $Multiplying trinomials and polynomials img 7$ , 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: $Multiplying trinomials and polynomials img 3$ .

2) $Multiplying trinomials and polynomials img 8$

$Multiplying trinomials and polynomials img 9$

$Multiplying trinomials and polynomials img 10$

First, we distribute the $Multiplying trinomials and polynomials img 11$ and get $Multiplying trinomials and polynomials img 12$

Next, we distribute the $Multiplying trinomials and polynomials img 13$ and get $Multiplying trinomials and polynomials img 14$

Then, we distribute the $Multiplying trinomials and polynomials img 15$ and get $Multiplying trinomials and polynomials img 16$

Now we have $Multiplying trinomials and polynomials img 17$ , but we are not finished because we can combine like terms. Combine them to get our final answer (in standard form): $Multiplying trinomials and polynomials img 18$ .

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) $Multiplying trinomials and polynomials img 19$

2) $Multiplying trinomials and polynomials img 20$

3) $Multiplying trinomials and polynomials img 21$

4) $Multiplying trinomials and polynomials img 22$

5) $Multiplying trinomials and polynomials img 23$

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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Multiplying Trinomials and Polynomials

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