How do you simplify #\frac { - 28a ^ { 5} b ^ { 2} + 32a ^ { 4} b ^ { 3} - 16a ^ { 3} b ^ { 3} } { - 4a ^ { 2} b ^ { 2} }#?

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Answer 1 · 2017-12-02T03:10:29

Expression #= 7a^3 - 8a^2b + 4ab#

Expression #=(-28a^5b^2+32a^4b^3-16a^3b^3)/(-4a^2b^2)#

We can break the expression up into three terms as follows:

Expression #=(-28a^5b^2)/(-4a^2b^2)+(32a^4b^3)/(-4a^2b^2)-(16a^3b^3)/(-4a^2b^2)#

#= +(7a^5b^2)/(a^2b^2)- (8a^4b^3)/(a^2b^2) + (4a^3b^3)/(a^2b^2)#

Applying the rule of indices: #a^m/a^n = a^(m-n)#

Now, assuming #{a,b}!=0#

Expression #=7a^(5-2)b^(2-2) - 8a^(4-2)b^(3-2) + 4a^(3-2)b^(3-2)#

#= 7a^3b^0 - 8a^2b^1+4a^1b^1#

#= 7a^3 - 8a^2b + 4ab#