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

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

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