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सिद्ध कीजिए कि (x + y + z)^2 – (x – y – z)^2 = 4x ( y + z)

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सिद्ध कीजिए कि (x + y + z)2 – (x – y – z)2 = 4x ( y + z)

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L.H.S. = (x + y + z)2 – (x – y – z)2

= x2 + y2 + z2 + 2(xy + yz + zx) 

– (x2 +  y2 + z2 – 2xy + 2yz – 2zx)

= 4xy + 4xz 

= 4x(y + z) = R.H.S.

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