Question

Expand:

`(a/2 + 2b - 4c)^2`

Answer 1

`(a/2 + 2b - 4c)^2`

Here, let a = `a/2`, b = 2b, c = −4c

Using the identity,

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

`(a/2 + 2b - 4c)^2 = (a/2)^2 + (2b)^2 + (-4c)^2 + 2(a/2)(2b) + 2(2b)(-4c) + 2(-4c)(a/2)`

= `a^2/4 + 4b^2 + 16c^2 + ((2a)/2)(2b) + 2(-8bc) + 2((-4ac)/2)`

= `a^2/4 + 4b^2 + 16c^2 + (a)(2b) - 16bc + 2(-2ac)`

∴ `a^2/4 + 4b^2 + 16c^2 + 2ab - 16bc - 4ac`