Expand each of the following, using suitable identities: (i) (x+2y+4z)^(2) (ii) (2x-y+z)^(2)

Expand First Expression: Step 1: Expand (x+2y+4z)^(2) using the identity (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. Calculation: (x+2y+4z)^2 = x^2 + (2y)^2 + (4z)^2 + 2*x*2y + 2*x*4z + 2*2y*4z = x^2 + 4y^2 + 16z^2 + 4xy + 8xz + 16yzExpand Second Expression: Step 2: Expand (2x-y+z)^(2) using the identity (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. Calculation: (2x-y+z)^2 = (2x)^2 + (-y)^2 + z^2 + 2*2x*(-y) + 2*2x*z + 2*(-y)*z = 4x^2 + y^2 + z^2 - 4xy + 4xz - 2yz

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Expand each of the following, using suitable identities:
(i)
(x+2y+4z)^(2)
(ii)
(2x-y+z)^(2)

Expand each of the following, using suitable identities: $\newline$ (i) $(x+2 y+4 z)^{2}$ $\newline$ (ii) $(2 x-y+z)^{2}$

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Algebra 2

Simplify rational expressions

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Q. Expand each of the following, using suitable identities:

\newline

(i)

(x+2 y+4 z)^{2}

\newline

(ii)

(2 x-y+z)^{2}

Expand First Expression: Step $1$ : Expand $(x+2y+4z)^{2}$ using the identity $(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$ . $\newline$ Calculation: $\newline$ $(x+2y+4z)^2 = x^2 + (2y)^2 + (4z)^2 + 2\cdot x\cdot 2y + 2\cdot x\cdot 4z + 2\cdot 2y\cdot 4z$ $\newline$ $= x^2 + 4y^2 + 16z^2 + 4xy + 8xz + 16yz$
Expand Second Expression: Step $2$ : Expand $(2x-y+z)^{2}$ using the identity $(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$ . $\newline$ Calculation: $\newline$ $(2x-y+z)^2 = (2x)^2 + (-y)^2 + z^2 + 2\cdot2x\cdot(-y) + 2\cdot2x\cdot z + 2\cdot(-y)\cdot z$ $\newline$ $= 4x^2 + y^2 + z^2 - 4xy + 4xz - 2yz$