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

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Solution

${(x + 2 y + 4 z)}^{2}$
Here a = x, b = 2y and x = 4z
= $x^{2}$ + ${(2 y)}^{2}$ + ${(4 z)}^{2}$ + 2x(2y) + 2(2y)(4z) + 2(4z)x
= $x^{2}$ + ${4 y}^{2}$ + ${16 z}^{2}$ + 4xy + 16yz + 8zx

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