Question

Cho các đa thức:

\(A=4x^2-5xy+3y^2\)

\(B=3x^2_{ }+2xy+y^2\)

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

Tính :

a, A + B + C

b, B - C - A

c, C - A - B

Answer 1

a/ \(A+B+C=\left(4x^2-5xy+3y^2\right)+\left(3x^2+2xy+y^2\right)+\left(2y^2+3xy-x^2\right)\)

\(=\left(4x^2+3x^2-x^2\right)+\left(-5xy+2xy+3xy\right)+\left(3y^2+y^2+2y^2\right)\)

\(=6x^2+6y^2\)

b/ \(B-C-A=\left(3x^2+2xy+y^2\right)-\left(2y^2+3xy-x^2\right)-\left(4x^2-5xy+3y^2\right)\)

\(=\left(3x^2+x^2-4x^2\right)+\left(2xy-3xy+5xy\right)+\left(y^2+2y^2-3y^2\right)\)

\(=-4xy\)

c/ \(C-A-B=\left(2y^2+3xy-x^2\right)-\left(4x^2-5xy+3y^2\right)-\left(3x^2+2xy+y^2\right)\)

\(=\left(2y^2-3y^2-y^2\right)+\left(3xy+5xy-2xy\right)+\left(-x^2+4x^2-3x^2\right)\)

\(=-2y+6xy\)