Question

(x+y+z)^2 + (x+y+z)^2

Answer 1

Question :-

$\sf(x + y + z)^{2} + (x + y + z)^{2}$

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Formula :-

$\sf(a + b + c)^{2} = a^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

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Solution :-

$\rm (x + y + z)^{2} + (x + y + z)^{2}$

Now, here

• A = X
• B = Y
• C = Z

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$\rm (x + y + z)^{2} + (x + y + z)^{2}$

$\rm\mapsto2(x + y + z) ^{2}$

Now, applying the formula ,

$\rm\mapsto2[(x) ^{2} + (y)^{2} +( z) ^{2} + 2(x)(y) + 2(y)(x) + 2(z)(x)]$

$\rm \mapsto2[ {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx$

$\rm \mapsto \bf \star \: \: 2{x}^{2} + 2{y}^{2} + 2{z}^{2} + 4xy + 4yz + 4zx$

${\huge\therefore} \: \: \rm (x + y + z)^{2} + (x + y + z)^{2} = \bf \: \: 2{x}^{2} + 2{y}^{2} + 2{z}^{2} + 4xy + 4yz + 4zx$

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