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Introduction to :

You have already started multiplying polynomials, but now we will take this a few steps further. Look at the examples carefully and make note of the exponents. Remember: 5xy means 5 x X x y

Again, it is helpful to think of subtraction as adding a negative: (x – 5) is the same as (x + -5). This will help you keep track of which terms are negative and which are positive.

Multiplying Monomial times Monomial

When multiplying a monomial by a monomial, multiply the coefficients together and tack on the variables on the end (usually in alphabetical order).

(14a)(2b) = 28ab

When multiplying two of the same variables, add the exponents. Remember that the exponent of x is 1.

x x^2 = x^1 x^2 = x^3

The reason for this is that x2 is really just x times x, and x times x2 is x times x times x, or xxx, which equals x3 (since there are three x's).

Multiplying Monomial times Polynomial

This is just the distributive property that you just learned. First we are going to change the subtraction symbol to adding a negative.

4x(6 + -2y)

Next we will distribute the 4x.

distribution arrows 4x(6 + -2y)


Example 1


X x 2X x 3X x 4X

Example 2


15(2x + 3y + -1)

Example 3


-4z(6 + 5z) + -3z

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