`1)VT=(x+y)²-y²`
`=x²+2xy+y²-y²`
`=(x²+2xy)+(y²-y²)`
`=x(x+2y)`
`=VP`
`⇒đpcm`
`2)VT=(x²+y²)²-(2xy)²`
`=(x²+y²+2xy)(x²+y²-2xy)`
`=(x+y)².(x-y)²`
`=VP`
`⇒đpcm`
`3)VP=x(x-3y)²+y(y-3x)²`
`=x(x²-6xy+9y²)+y(y²-6xy+9x²)`
`=x³-6x²y+9xy²+y³-6xy²+9x²y`
`=x³+(-6x²y+9x²y)+(9xy²-6xy²)+y³`
`=x³+3x²y+3xy²+y³`
`=(x+y)³`
`=VT`
`⇒đpcm`
`4)VT=(a+b)³+(a-b)³`
`=(a+b+a-b)[(a+b)²-(a+b)(a-b)+(a-b)²]`
`=2a[a²+2ab+b²-(a²-b²)+a²-2ab+b²]`
`=2a(a²+2ab+b²-a²+b²+a²-2ab+b²)`
`=2a[(a²-a²+a²)+(2ab-2ab)+(b²+b²+b²)]`
`=2a(a²+3b²)`
`=VP`
`⇒đpcm`
`5)VT=(a+b)³-3ab(a+b)`
`=(a+b)[(a+b)²-3ab]`
`=(a+b)(a²+2ab+b²-3ab)`
`=(a+b)(a²-ab+b²)`
`=a³-b³`
`=VP`
`⇒đpcm`
`6)VT=(a-b)³+3ab(a-b)`
`=(a-b)[(a-b)²+3ab]`
`=(a-b)(a²-2ab+b²+3ab)`
`=(a-b)(a²+ab+b²)`
`=a³-b³`
`=VP`
`⇒đpcm`
`7)VT=(a²+b²)²-2a²b²`
`=(a²)^2+2a²b²+(b²)^2-2a²b²`
`=a^4+(2a²b²-2a²b²)+b^4`
`=a^4+b^4`
`=VP`
`⇒đpcm`
`8)VT=(a+b+c)²`
`=[(a+b)+c]²`
`=(a+b)²+2c(a+b)+c²`
`=a²+2ab+b²+2ca+2bc+c²`
`=a²+b²+c²+(2ab+2bc+2ca)`
`=a²+b²+c²+2(ab+bc+ca)`
`=VP`
`⇒đpcm`
`9)VP=(x-y)(x^4+x³y+x²y²+xy³+y^4)`
`=x^5+x^4y+x³y²+x²y³+xy^4-x^4y-x³y²-x²y³-xy^4-y^5`
`=x^5+(x^4y-x^4y)+(x³y²-x³y²)+(x²y³-x²y³)+(xy^4-xy^4)-y^5`
`=x^5-y^5`
`=VT`
`⇒đpcm`
`10)VP=(x+y)³-3xy(x+y)`
`=(x+y)[(x+y)²-3xy]`
`=(x+y)(x²+2xy+y²-3xy)`
`=(x+y)(x²-xy+y²)`
`=VT`
`⇒đpcm`