Question

Rút gọn:
a) A=(5-x)(5+x)-x(4-x)-25
b) B=(x²+1)(x+1)-(x+1)³
c) C=(x+y-2)²-2(x+y-2)(y+x)+(x+y)²

Answer 1

a) \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25\\ =25-x^2-4x+x^2-25\\ =-4x\)

b) \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3\\ =x^3+x+x^2+1-x^3-3x^2-3x-1\\ =-2x^2-2x\)

c) \(\left(x+y-2\right)^2-2\left(x+y-2\right)\left(y+x\right)+\left(x+y\right)^2\)

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

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

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

\(=4\)

Answer 2

a) \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25=25-x^2-4x+x^2-25=-4x\)b) \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3=\left(x+1\right)\left[x^2+1-\left(x+1\right)^2\right]=\left(x+1\right)\left(x^2+1-x^2-2x-1\right)=\left(x+1\right)\left(-2x\right)\)c) \(C=\left(x+y-2\right)^2-2\left(x+y-2\right)\left(y+x\right)+\left(x+y\right)^2=\left(x+y-1-x-y\right)^2=\left(-1\right)^2=1\)

 

 

Answer 3

a: Ta có: \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25\)

\(=5-x^2-4x+x^2-25\)

=-4x-20

b: Ta có: \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3\)

\(=x^3+x+x^2+1-x^3-3x^2-3x-1\)

\(=-2x^2-2x\)