Multiplying Monomials

 Multiplying monomials involves two steps: 1) Multiply the numbers (coefficients) 2) Multiply the variables. Remember that when you multiply powers, you add the exponents. Examples: 1) 3x.5x=15x2 First you multiply 3.5=15. Then x.x=x2 2) 4y3.2y2=8y5 4.2=8 y3.y2=y5 because when you multiply powers you add the exponents (because if you were to write it out you have y.y.y.y.y=y5). 3) 2x(-8x2 )=-16x3 2(-8)=-16. x.x2=x3 . Remember that any variable with no exponent has an understood exponent of 1, so this is like x1.x2=x3. To multiply powers, add the exponents. 1+2=3. 4) -4x2 y(7x4 y3 )=-28x6 y4 Notice that first the numbers are multiplied, then the x's (2+4=6), then the y's (understood 1+3=4) 5) 3x(4y)=12xy. Notice the numbers were multiplied then the variables were both included in the answer. Practice: Multiply the monomials 1) 3y2 (5y) 2) -2x5 (-9x) 3) 7x2 y(4x3 y4) 4) 3x(4x)(2x) 5) 5x2 (-8y) Answers: 1) 15y3 2) 18x6 3) 28x5 y5 4) 24x3 5) -40x2 y

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