`#AkaShi`
`a) (a+b)^2=(a-b)^2+4ab`
Xét vế phải
`(a-b)^2+4ab=a^2-2ab+b^2+4ab=a^2+2ab+b^2=(a+b)^2`
`⇒đpcm`
....................
`b) (a-b)^2=(a+b)^2-4ab`
Xét vế phải:
`(a+b)^2-4ab=a^2+2ab+b^2-4ab=a^2-2ab+b^2=(a-b)^2`
`⇒đpcm`
..................
`c) (a²+b²)(x²+y²)=(ax-by)²+(ay+bx)²`
Xét vế phải:
`(ax-by)²+(ay+bx)²`
`=a²x²-2axby+b²y²+ay²+2axby+bx²`
`=a²x²+a²y²+b²x²+b²y²`
`=a²(x²+y²)+b²(x²+y²)`
`=(x²+y²)(a²+b²)`
`⇒đpcm`
