Q4 of 86 Page 56

Expand each of the following, using suitable identities

(x + 2y + 4z)2

Using (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


Here a = x, b = 2y and c = 4z


⇒ (x + 2y + 4z)2 = x2 + (2y)2 + (4z)2 + 2(x)(2y) + 2(2y)(4z) + 2(4z)(x)


Therefore


(x + 2y + 4z)2 = x2 + 4y2 + 16z2 + 4xy + 16yz + 8xz


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