How do you find the product #(m+2)[(m^2+3m-6)+(m^2-2m+4)]#?

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Answer 1 · 2018-03-30T02:28:05

#(m+2)[(m^2+3m-6)+(m^2-2m+4)]=color(blue)(2m^3+5m^2-4#

Given:

#(m+2)[(m^2+3m-6)+(m^2-2m+4)]#

Simplify the brackets.

#(m+2)(m^2+3m-6+m^2-2m+4)#

Collect like terms.

#(m+2)((m^2+m^2)+(3m-2m)+(-6+4))#

Combine like terms.

#(m+2)(2m^2+m-2)#

Distribute #(color(blue)(m+2))#.

#2m^2(color(blue)(m+2))+m(color(blue)(m+2))-2(color(blue)(m+2))=#

#2m^3+4m^2+m^2+2m-2m-4#

Collect like terms.

#2m^3+(4m^2+m^2)+(2m-2m)-4#

Combine like terms.

#2m^3+5m^2-4#