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.

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

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