Question

Expand each of the following, using suitable identities:
(i) `(x+2y+4z)^2` (ii) `(2x-y+z)^2` (iii) `(-2x+3y+2z)^2`
(iv) `(3a-7b-c)^2`(v) `(-2x+5y-3z)^2` (vi) `[1/4a-1/2b+1]^2`

Answer 1

Here, we will use the identity,
`(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca`
(i) `(x+2y+4z)^2 = x^2+(2y)^2+(4z)^2+2(x)(2y)+2(2y)(4z)+2(4z)(x)`
`=x^2+4y^2+16z^2+4xy+16yz+8zx`
(ii) `(2x-y+z)^2 = (2x)^2+(-y)^2+(z)^2+2(2x)(-y)+2(-y)(z)+2(z)(2x)`
`=4x^2+y^2+z^2-4xy-2yz+4zx`
Similarly, we can solve the other parts.