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Show that : (i) (4p q+3q)^2-(4q p-3q)^...

Show that :
(i) `(4p q+3q)^2-(4q p-3q)^2=48 p q^2`
(ii) `(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0`

Text Solution

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Given:
`(i) (4p q+3q)^2-(4q p-3q)^2=48 p q^2`
`=> (4pq)^2+(3q)^2+2(4pq)(3q)- (4pq)^2+(3q)^2-2(4pq)(3q)=48 p q^2`
`=> 16p^2q^2+9q^2+24pq^2- 16p^2q^2-9q^2+24pq^2(3q)=48 p q^2`
`=> 24pq^2+24pq^2=48 p q^2`
`=> 48pq^2=48 p q^2`
`=> LHS=RHS`
`(ii) (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0`
...
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