What is #24x ^ { 2} y ^ { 6} - 16x ^ { 6} y ^ { 2} + 4x y ^ { 2}# divided by #4xy^2#?

1 Answer
smendyka
May 30, 2017

See a solution process below:

Explanation:

First, we can write this expression as:

#(24x^2y^6 - 16x^6y^2 + 4xy^2)/(4xy^2)#

Or

#(24x^2y^6)/(4xy^2) - (16x^6y^2)/(4xy^2) + (4xy^2)/(4xy^2)#

Next, we can cancel common terms in each of the fractions:

#(color(red)(cancel(color(black)(24)))6color(green)(cancel(color(black)(x^2)))xcolor(purple)(cancel(color(black)(y^6)))y^4)/(color(red)(cancel(color(black)(4)))color(green)(cancel(color(black)(x)))color(purple)(cancel(color(black)(y^2)))) - (color(red)(cancel(color(black)(16)))4color(green)(cancel(color(black)(x^6)))x^5color(purple)(cancel(color(black)(y^2))))/(color(red)(cancel(color(black)(4)))color(green)(cancel(color(black)(x)))color(purple)(cancel(color(black)(y^2)))) + color(red)(cancel(color(black)(4xy^2)))/color(red)(cancel(color(black)(4xy^2))) =>#

#6xy^4 - 4x^5 + 1#

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