How do you multiply #(m + 9) ( m ^ { 2} + 3m - 5)#?

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Answer 1 · 2017-06-04T01:16:55

#m^3 + 12m^2 + 22m - 45#

Use the distributive property to separate #(m+9)#:

#(color(red)m+color(blue)9)(m^2+3m-5)#

#= color(red)m(m^2+3m-5) + color(blue)9(m^2+3m-5)#

Now, use the distributive property again to distribute the #color(red)m# and #color(blue)9#.

#= (color(red)m*m^2+color(red)m*3m-color(red)m*5)+(color(blue)9*m^2+color(blue)9*3m-color(blue)9*5)#

#= (m^3 + 3m^2 - 5m) + (9m^2 + 27m - 45)#

Finally, combine like terms and simplify:

#(m^3) + (3m^2 + 9m^2) + (-5m+27m) + (-45)#

#m^3 + 12m^2 + 22m - 45#

Final Answer