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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+2y+4z)2 (x+2 y+4 z)^{2} \newline(ii) (2x−y+z)2 (2 x-y+z)^{2}

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Full solution

Q. Expand each of the following, using suitable identities:\newline(i) (x+2y+4z)2 (x+2 y+4 z)^{2} \newline(ii) (2x−y+z)2 (2 x-y+z)^{2}
  1. Expand First Expression: Step 11: Expand (x+2y+4z)2(x+2y+4z)^{2} using the identity (a+b+c)2=a2+b2+c2+2ab+2ac+2bc(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc.\newlineCalculation: \newline(x+2y+4z)2=x2+(2y)2+(4z)2+2⋅x⋅2y+2⋅x⋅4z+2⋅2y⋅4z(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=x2+4y2+16z2+4xy+8xz+16yz= x^2 + 4y^2 + 16z^2 + 4xy + 8xz + 16yz
  2. Expand Second Expression: Step 22: Expand (2x−y+z)2(2x-y+z)^{2} using the identity (a+b+c)2=a2+b2+c2+2ab+2ac+2bc(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc.\newlineCalculation:\newline(2x−y+z)2=(2x)2+(−y)2+z2+2⋅2x⋅(−y)+2⋅2x⋅z+2⋅(−y)⋅z(2x-y+z)^2 = (2x)^2 + (-y)^2 + z^2 + 2\cdot2x\cdot(-y) + 2\cdot2x\cdot z + 2\cdot(-y)\cdot z\newline=4x2+y2+z2−4xy+4xz−2yz= 4x^2 + y^2 + z^2 - 4xy + 4xz - 2yz

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