Question

simplify (x+y+z)^2+(x-y-z)^2​

Answer 1

Answer:

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Step by step solution:

$(x+y+z)^2+(x-y-z)^2\\\\we \ have \ to \ solve \ it.\\\\Let \ us \ do\\\\using \ identity \ (a+b+c)^2=(a^2+b^2+c^2+2ab+2bc+2ca)\\\\ (x+y+z)^2+(x-y-z)^2= (x+y+z)^2+(x+(-y)+(-z))^2\\\\ (x+y+z)^2+(x-y-z)^2=[(x^2+y^2+z^2+2xy+2yz+2xz+x^2+y^2+z^2+(2x \times-y)+(2 \times-y \times-z)+(2x \times-z)]\\\\(x+y+z)^2+(x-y-z)^2= (2x^2+2y^2+2z^2+2xy+2yz+2xz-2xy+2yz-2xz)\\\\x+y+z)^2+(x-y-z)^2=(2x^2+2y^2+2z^2+2yz)\\\\x+y+z)^2+(x-y-z)^2=2(x^2+y^2+z^2+yz)$

Hope it is clear to you.