Question

subtract:2x³-3xy²+6x²y-5y³ from -x³+8xy²-16x²y+y³​

Answer 1

$Let's \: simplify \: step-by-step.$

$−x {}^{3} +8xy {}^{2} −16 {x}^{2} y+y {}^{3} −(2x {}^{3} −3x {y}^{2} +6 {x}^{2} y−5 {y}^{3} )$

$Distribute \: the \: Negative \: Sign:$

$=− {x}^{3} +8x {y}^{2} +−16 {x}^{2} y+ {y}^{3} +−1(2 {x}^{3} )+−1(−3x {y}^{2} )+−1(6 {x}^{2} y)+−1(−5 {y}^{3} )$

$=− {x}^{3} +8x {y}^{2} +−16 {x}^{2} y+ {y}^{3} +−2 {x}^{3} +3x {y}^{2} +−6 {x}^{2} y+5 {y}^{3}$

$Combine \: Like \: Terms:$

$=(− {x}^{3} +−2 {x}^{3} )+(−16 {x}^{2} y+−6 {x}^{2} y)+(8xy {y}^{2} +3x {y}^{2} )+( {y}^{3} +5 {y}^{3} )$

$=−3 {x}^{3} +−22 {x}^{2} y+11xy {}^{2} +6 {y}^{3}$