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Multiplying Monomials

Monomials

Amonomialis a number, a variable, or a product of a number and one or more variables.

The only rules are that the variables should be raised to only positive integer powers (nosquare rootsor 1 x 's allowed), and no plus or minus signs.

Examples:

17 , 3 x y , − 4 x 2 ,

7 100 a 5 b 6 c 7 d 8 z 999

Multiplication of Monomials

When you multiply monomials, first multiply the coefficients and then multiply the variables by adding theexponents.

Examples:

1 ) 4 2 ⋅ 4 3 = 4 2 + 3 = 4 5 2 ) x 2 ⋅ x 5 = x 2 + 5 = x 7 3 ) 4 2 ⋅ x 5 = 16 ⋅ x 5 = 16 x 5 4 ) ( − 2 a 2 b ) ( 5 a 3 b 2 ) = ( − 2 ⋅ 5 ) ( a 2 + 3 ) ( b 1 + 2 ) = − 10 a 5 b 3 5 ) ( − 2 a 2 b ) ( 5 a 3 b 2 ) ( a b c ) = ( − 2 ⋅ 5 ) ( a 2 + 3 + 1 ) ( b 1 + 2 + 1 ) ( c ) = − 10 a 6 b 4 c

Note that when you multiply monomials with same base, you can add their exponents.

a m ⋅ a n = a m + n

This is called theProduct of Powers Property.