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Multiplying Polynomials

Q: Multiply -9m(2m2 + 6m – 1)

A:  When adding and subtracting polynomials, you can only combined like terms.  This is not the case with multiplication.  You can multiply unlike terms together.

-9m(2m2 + 6m – 1)

In this problem the whole quantity in the parentheses is being multiplied by -9m.  So, -9m needs to multiply each term:

-9m(2m2 + 6m – 1) = -9m*2m2 + -9m*6m + -9m*-1
Now we need to clean up the expression on the right:

-9m*2m2 + -9m*6m + -9m*-1 ….

-9m*2m2 can be thought of as -9*m*2*m*m = -18m3

(multiply the coefficients together, and multiply the m’s together)

-9m*6m = -54m2

-9m*-1 = 9m

So, final answer cleans up like:

-9m(2m2 + 6m – 1) = -18m3 – 54m2 + 9m

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