Question

216. Cho \(A=xy-3xy\left(1+x-y\right)+x^2\left(x+1\right)-y^2\left(y-1\right)\)

a) Rút gọn A

b) Tính A khi x-y=5

Answer 1

a) \(A=xy-3xy\left(1+x-y\right)+x^2\left(x+1\right)-y^2\left(y-1\right)\)

\(A=xy-3xy-3x^2y+3xy^2+x^3+x^2-y^3+y^2\)

\(A=x^2-2xy+y^2+x^3-3x^2y+3xy^2-y^3\)

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

b) Khi x-y =5

<=> x= 5+y

Thay vào bt A ,ta được:

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

\(A=5^2+5^3=25+125=150\)

Answer 2

\(A=xy-3xy\left(1+x-y\right)+x^2\left(x+1\right)-y^2\left(y-1\right)\)

\(A=xy-3xy-3x^2y+3xy^2+x^3+x^2-y^3+y^2\)

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

\(A=\left(x-y\right)^2\left(x-y+1\right)\)

b) Với x - y = 5 ta có

\(A=5^2.6=150\)