Question

Thu gọn đa thức :

\(A=2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\)

với \(x=a^2+2ab+b^2\) , y \(=a^2-2ab+b^2\)

Answer 1

\(A=2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\)

\(=2y-x-\left\{2x-y-\left[y+3x-5y+x\right]\right\}\)

\(=2y-x-\left\{2x-y-y-3x+5y-x\right\}\)

\(=2y-x-2x+y+y+3x-5y+x\)

\(=\left(2y+y+y-5y\right)+\left(-x-2x+3x+x\right)\)

= \(-y+x\)

Thay \(x=a^2+2ab+b^2,y=a^2-2ab+b^2\) vào đa thức -y + x :

\(-\left(a^2-2ab+b^2\right)+\left(a^2+2ab+b^2\right)\)

\(=-a^2+2ab-b^2+a^2+2ab+b^2\)

\(=\left(-a^2+a^2\right)+\left(2ab+2ab\right)+\left(-b^2+b^2\right)\)

= 4ab

Answer 2

\(A=2y-x-\left\{2x-y-\left[y+3x-\left(5y-x\right)\right]\right\}\\ =2y-x-\left\{2x-y-y-3x+5y-x\right\}\\ =2y-x-2x+y+y+3x-5y+x\\ =-y+x=-\left(a^2-2ab+b^2\right)+\left(a^2+2ab+b^2\right)\\ =-a^2+2ab-b^2+a^2+2ab+b^2=4ab\)