How do you multiply #(10x^2-13xy-3y^2)/(8x^2-10xy-3y^2)*(2y+8x)/(2x^2+2y^2)#?

2 Answers
Apr 11, 2018

Answer:

#{40x^3-42x^2y - 25xy^2 - 3y^3 }/{8x^4 - 10x^3y + 5x^2y^2 - 10xy^3 - 3y^4)#

Explanation:

#{(10x^2 - 13xy - 3y^2)(2y+8x)}/{(8x^2 - 10xy - 3y^2)(2x^2 + 2y^2)}=#

#{2y(10x^2 - 13xy - 3y^2)+8x(10x^2 - 13xy - 3y^2)}/{2x^2(8x^2 - 10xy - 3y^2) + 2y^2(8x^2 - 10xy - 3y^2))#

#{2y10x^2 - 2y13xy - 2y3y^2 +8x10x^2 - 8x13xy - 8x3y^2}/{2x^2 8x^2 - 2x^2 10xy - 2x^2 3y^2 + 2y^2 8x^2 - 2y^2 10xy - 2y^2 3y^2)#

This can be simplified to:

#{10x^2y - 13xy^2 - 3y^3 +40x^3 - 52x^2y - 12xy^2}/{8x^4 - 10x^3y - 3x^2y^2 + 8x^2y^2 - 10xy^3 - 3y^4)#

and further:

#{40x^3-42x^2y - 25xy^2 - 3y^3 }/{8x^4 - 10x^3y + 5x^2y^2 - 10xy^3 - 3y^4)#

Apr 11, 2018

Answer:

#color(magenta)(80x^3-84x^2y-50xy^2-6y^3)/(color(blue)(16x^4-20x^3y+10x^2y^2-20xy^3-6y^4)#

Explanation:

#(10x^2-13xy-3y^2)/(8x^2-10xy-3y^2)*(2y+8x)/(2x^2+2y^2)#

#color(white)(aaaaaaaaaaaaa)##10x^2-13xy-3y^2#
#color(white)(aaaaaaaaaaa)## xx underline(2y+8x)#
#color(white)(aaaaaaaaaaaaa)##20x^2y-26xy^2-6y^3#
#color(white)(aaaaaaaaaaa)##-104x^2y-24xy^2+0+80x^3#
#color(white)(aaaaaaaaaaaaa)##overline(-84x^2y-50xy^2-6y^3+80x^3)#

#color(white)(aaaaaaaaaaaaa)##color(magenta)(80x^3-84x^2y-50xy^2-6y^3#

#color(white)(aaaaaaaaaaaaa)##8x^2-10xy-3y^2#
#color(white)(aaaaaaaaaaa)## xx underline(2x^2+2y^2)#
#color(white)(aaaaaaaaaaaaa)##16x^4-20x^3y-6x^2y^2#
#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaa)##16x^2y^2-20xy^3-6y^4#
#color(white)(aaaaaaaaaaaaa)##overline(16x^4-20x^3y+10x^2y^2-20xy^3-6y^4)#

#color(white)(aaaaaaaaaaaaa)##color(blue)(16x^4-20x^3y+10x^2y^2-20xy^3-6y^4#

#color(white)(aaaaaaaaaaaaa)##color(magenta)((80x^3-84x^2y-50xy^2-6y^3)/color(blue)(16x^4-20x^3y+10x^2y^2-20xy^3-6y^4#