Question

thu gọn các biểu thức sau:

a)  2(x-1)(x+1)+(x-1)^2+(x+1)^2

b)  (x-y+1)²+(1-y)²+2(x-y+1)(y-1)

c)   (3x+1)²-2(3x+1)(3x+5)+(5x+5)²

 

 

Answer 1

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

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

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

\(b,\left(x-y+1\right)^2+\left(1-y\right)^2+2\left(x-y+1\right)\left(y-1\right)\)

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

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

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

đề cuối phải sửa cái cuối thành \(\left(3x+5\right)^2\) 

\(c,\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)

\(=\left[\left(3x+1\right)-\left(3x+5\right)\right]^2=\left[3x+1-3x-5\right]^2=16\)