Question

Thực hiện các phép tính sau:

a,(x+1)(x-2)

b,(4x⁴y⁴ -12x²y²):4x²y²

c,3x​​²-1/2x + x²+1/2x

d, x²/x-1 + 2x/1-x + 1/x-1

Cho x-y = 4 và x² + y²=106

Tính x³ - y³ 

Answer 1

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

b ) \(\left(4x^4y^4-12x^2y^2\right):4x^2y^2=x^2y^2-3\)

c ) \(\frac{3x^2-1}{2x}+\frac{x^2+1}{2x}=\frac{3x^2-1+x^2+1}{2x}=\frac{4x^2}{2x}=2x\)

d ) \(\frac{x^2}{x-1}+\frac{2x}{1-x}+\frac{1}{x-1}=\left(\frac{x^2}{x-1}+\frac{1}{x-1}\right)+\frac{2x}{1-x}\)

                                                     \(=\frac{x^2+1}{x-1}+\frac{2x}{1-x}=\frac{x^2+1}{x-1}+\frac{-2x}{x-1}=\frac{x^2+1-2x}{x-1}=\frac{\left(x-1\right)^2}{x-1}=x-1\)

Answer 2

a)   .......=x²-x-2

b)   .........=x²y²-3

c) .......=(3x²-1+x²+1)/2x=4x²/2x=2x

d) x² /(x-1)+(-2x)/(x-1)+1/(x-1)=(x²-2x+1)/(x-1)=(x-1)²/(x-1)=x-1

e)...

x-y=4

=> x²-2xy+y²=16

 <=> 106-2xy =16  (vì x²+y² =106)

=>xy=(106-16)/2=45

ta có   x³ -y³ =(x-y)(x²+xy+y² )

=4(106+45)=604

Answer 3

a,(x+1)(x-2)=x^2-x-2

b,(4x⁴y⁴ -12x²y²):4x²y^{2=x^2.y^2-3}