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find the following products (i) ((x...

find the following products
`(i) ((x)/(2)+2y)((x^(2))/(4)-xy+4y^(2))`(ii) `(x^(2)-1)(x^(4)+x^(2)+1)`

Text Solution

Verified by Experts

We have
`(i) ((x)/(2)+2y)((x^2)/(4)-xy+4y^2)`
`=(a+b)(a^2-ab)+b^2)," where " (x)/(2)=a and 2y=b`
`=(a^3+b^3)`
`=((x)/(2))^3+(2y)^3=((x^3)/(8)+8y^3)`.
` (ii) (x^2-1) (x^4+x^2+1)`
` =(a-b(a^2+ab+b^2), " where " x^2=a and 1=b`
` =(a^3-b^3)`
`=(x^2)^3-(1)^3=(x^6-1)`.
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