Using the identity #160; (a+b+c)^ 2 =a^ 2 +b^ 2 +c^ 2 +2ab+2bc+2ca .GIven: #160; (x+y+3z)^2 #160;we apply the above identity as follows: (x+ ...

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Algebraic Identities

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Question

Expand: ${(x + y + 3 z)}^{2}$

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Solution

Using the identity $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ .

GIven: $(x + y + 3 z)^{2}$ we apply the above identity as follows:

$(x + y + 3 z)^{2} = x^{2} + y^{2} + (3 z)^{2} + (2 \times x \times y) + (2 \times y \times 3 z) + (2 \times 3 z \times x) = x^{2} + y^{2} + 9 z^{2} + 2 x y + 6 y z + 6 z x$

Hence, $(x + y + 3 z)^{2} = x^{2} + y^{2} + 9 z^{2} + 2 x y + 6 y z + 6 z x$ .

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