a, (x-2)^2 - (x+2)^2
=x2-4x+4-x2-4x-4
=-8x
b, ( x-1/2).(x+1/2)+1/4
\(=x^2-\frac{1}{4}+\frac{1}{4}\)
\(=x^2\)
c, (x-1)(x2+x+1)-x2(x-1)
=(x-1)*[(x2+x+1)-x2]
=(x-1)(x2+x+1-x2)
=(x-1)(x+1)
=x2-1
d,4(x-y)(x+y)+(x-y)2+(2x+2y)2
=4(x-y)(x+y)+(x-y)2+4(x+y)2
=(x+y)[4(x-y)+4(x+y)]+(x-y)2
=(x+y)[4x-4y+4x+4y]+x2-2xy+y2
=(x+y)8x+x2-2xy+y2
=8x2+8xy+x2-2xy+y2
=9x2+6xy+y2
Bài 2:
a)x2+6x+11
=x2+6x+9+2
=(x+3)2+2
Ta thấy: \(\left(x+3\right)^2\ge0\) với mọi x
\(\Rightarrow\left(x+3\right)^2+2\ge2>0\) với mọi x
b, 10x-x2-26
=-x2+10x-25-1
=-(x2-10x+25)-1
=-(x-5)2-1
Ta thấy:\(\left(x-5\right)^2\ge0\) với mọi x
\(\Rightarrow-\left(x-5\right)^2\le0\) với mọi x
\(\Rightarrow-\left(x-5\right)^2-1\le-1< 0\) với mọi x
