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=15x^{2} First you multiply 3.5=15. Then x.x=x^{2} 2) 4y^{3}.2y^{2}=8y^{5} 4.2=8 y^{3}.y^{2}=y^{5} because when you multiply powers you add the exponents (because if you were to write it out you have y.y.y.y.y=y^{5}). 3) 2x(-8x^{2} )=-16x^{3} 2(-8)=-16. x.x^{2}=x^{3} . Remember that any variable with no exponent has an understood exponent of 1, so this is like x^{1}.x^{2}=x^{3}. To multiply powers, add the exponents. 1+2=3. 4) -4x^{2} y(7x^{4} y^{3} )=-28x^{6} y^{4} 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) 3y^{2} (5y) 2) -2x^{5} (-9x) 3) 7x^{2} y(4x^{3} y^{4}) 4) 3x(4x)(2x) 5) 5x^{2} (-8y) Answers: 1) 15y^{3} 2) 18x^{6} 3) 28x^{5} y^{5} 4) 24x^{3} 5) -40x^{2} y |