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# Polynomials

## Multiplication

Multiplication of polynomials is also known as "expanding the brackets".   In multiplying two polynomials we will make use of the distributive law: a(b + c) = ab + ac

First let's try multiplying a single term to a polynomial:

3(2x + 5) = 3(2x) + 3(5) = 6x + 15

x(-x + 2) = x(-x) + x(2) = -x2 + 2x

x2(3x + 5) = x2(3x) + x2(5) = 3x3 + 5x2

### Exercise 5.

 Polynomial 1 Polynomial 2 Product

More generally,

(a +b)(c + d) = a(c + d) +b(c + d)
= ac + ad +bc + bd

i.e. we multiply each term in the first brackets by each term in the second brackets and add.

### Example 3.

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Note: The degree of the product of two polynomials is equal to the sum of the degrees of the given polynomials.

### Exercise 6.

 Polynomial 1 Polynomial 2 Product

### Example 4.

When one of the given polynomials contains three or more terms it is easier to present the multiplication as follows.

Multiply :

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