Expand the following, using suitable identities: ${(x + 2 y + 4 z)}^{2}$

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Solution

Answer:
Given ${(x + 2 y + 4 z)}^{2}$
Using identity, ${(x + y + z)}^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x$
Here, $x = x, y = 2 y, z = 4 z$
${(x + 2 y + 4 z)}^{2} = x^{2} + {(2 y)}^{2} + {(4 z)}^{2} + (2 \times x \times 2 y) + (2 \times 2 y \times 4 z) + (2 \times 4 z \times x)$
${(x + 2 y + 4 z)}^{2} = x^{2} + 4 y^{2} + 16 z^{2} + 4 x y + 16 y z + 8 x z$

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