Write the following in the expanded form: `(a+2b+c)^2` (ii) `(2a-3b-c)^2`

Explanation

(i) `(a+2b+c)^2`
Using the identity, `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca`:
`(a+2b+c)^2`
`=a^2+(2b)^2+c^2+2a(2b)+2(2b)c+2ca`
`=a^2+4b^2+c^2+4ab+4bc+2ac`
`therefore (a+2b+c)^2=a^2+4b^2+c^2+4ab+4bc+2ac`

(ii) `(2a-3b-c)^2`
Using the identity, `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca`:
`=[(2a)+(−3b)+(−c)]^2`
`=(2a)^2+(−3b)^2+(−c)^2+2(2a)(−3b)+2(−3b)(−c)+2(2a)(−c)`
`=4a^2+9b^2+c^2−12ab+6bc−4ca`
`therefore (2a-3b-c)^2=4a^2+9b^2+c^2−12ab+6bc−4ca`