Question

How do you find the quotient of `(64x^2y^3z(2x - 8)( 3y^2 + 15y)) ÷ (12xy(y + 5)(x – 4))`?

Answer 1

`32xy^3z`

Explanation:

`(color(magenta)(64x^2y^3z)color(red)(""(2x-8))color(blue)(""(3y^2+15y)))/(color(magenta)(12xy)color(blue)(""(y+5))color(red)(""(x-4)))`

`=color(magenta)((16xy^2z)(4xy))/color(magenta)(3(4xy))xxcolor(red)(2(x-4))/color(red)((x-4))xxcolor(blue)(3y(y+5))/color(blue)((y+5))`

...and provided `x!=0 and y!=0 and x!=4 and y!=-5`

`=color(magenta)(16xy^2z)/color(magenta)cancel(3)xxcolor(red)2/color(white)1xxcolor(blue)(cancel(3)y)/color(white)(1)`

`=32xy^3z`