Multiplying monomials involves two steps:
1) Multiply the numbers (coefficients)
2) Multiply the variables. Remember that when you multiply powers, you add the exponents.
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)
5) 5x2 (-8y)
Answers: 1) 15y3 2) 18x6 3) 28x5 y5 4) 24x3 5) -40x2 y