Bài 3:
`a)VT=(a-b+c)²`
`=[(a-b)+c]²`
`=(a-b)²+2.(a-b).c+c²`
`=a²-2ab+b²-2ac-2bc+c²`
`=a²+b²+c²-2ab-2bc-2ac`
`=VP`
`⇒đpcm`
`b)VT=(a+b-c)²`
`=[(a+b)-c]²`
`=(a+b)²-2.(a+b).c+c²`
`=a²+2ab+b²-2ac-2bc+c²`
`=a²+b²+c²+2ab-2bc-2ac`
`=VP`
`⇒đpcm`
`c)VT=(a-b-c)²`
`=[(a-b)-c]²`
`=(a-b)²-2.(a-b).c+c²`
`=a²-2ab+b²-2ac+2bc+c²`
`=a²+b²+c²-2ab+2bc-2ac`
`=VP`
`⇒đpcm`
`d)VT=(a+b+c)²+a²+b²+c²`
`=[(a+b)+c]²+a²+b²+c²`
`=(a+b)²+2.(a+b).c+c²+a²+b²+c²`
`=a²+2ab+b²+2ca+2bc+c²+a²+b²+c²`
`=(a²+2ab+b²)+(b²+2bc+c²)+(c²+2ca+a²)`
`=(a+b)²+(b+c)²+(c+a)²`
`=VP`
`⇒đpcm`
Bài 4:
`A=(x-y)²+(x+y)²`
`=x²-2xy+y²+x²+2xy+y²`
`=(x²+x²)+(-2xy+2xy)+(y²+y²)`
`=2x²+2y²`
`B=(2x-1)²-2(2x-3)²+4`
`=4x²-4x+1-2(4x²-12x+9)+4`
`=4x²-4x+1-8x²+24x-18+4`
`=(4x²-8x²)+(-4x+24x)+(1-18+4)`
`=-4x²+20x-13`
`C=(x-1)²-2(x-1)(x-3)+(x-3)²`
`=[(x-1)-(x-3)]²`
`=(x-1-x+3)²`
`=2²`
`=4`
`D=(x-y+z)²+(z-y)²+2(x-y+z)(y-z)`
`=(x-y+z)²+2(x-y+z)(y-z)+(z-y)²`
`=(x-y+z)²+2(x-y+z)(y-z)+(y-z)²`
`=(x-y+z+y-z)²`
`=x²`
