Question

Rút gọn biểu thức

B = 2(x+y)(x-y) - (x-y)^2 + (x+y)^2 - 4y^2

C = (X-5)(2x+3) - 2x(x-3) + x-7

Answer 1

\(B=2\left(x+y\right)\left(x-y\right)-\left(x-y\right)^2+\left(x+y\right)^2-4y^2\)

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

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

\(=2x^2-6y^2+4xy\)

\(C=\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x-7\)

\(=x\left(2x+3\right)-5\left(2x+3\right)-2x^2+6x+x-7\)

\(=2x^2+3x-10x-15-2x^2+6x+x-7\)

\(=-22\)

Answer 2

Ta có: \(B=2\left(x+y\right)\left(x-y\right)-\left(x-y\right)^2+\left(x+y\right)^2-4y^2\)

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

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

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

Ta có: \(C=\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x-7\)

\(=2x^2+3x-10x-15-2x^2+6x+x-7\)

\(=-22\)