= (ab)(a^2 2 abb^2 3 ab)
= (ab)(a^2 abb^2 )
Example 12. Find the cube of 2 x 3 y.
Solution :( 2 x 3 y)^3 ( 2 x)^3 3 ( 2 x)^2 3 y 3 2 x( 3 y)^2 ( 3 y)^3
= 8 x^3 3 4 x^2 3 y 3 2 x 9 y^2 27 y^3
= 8 x^3 36 x^2 y 54 xy^2 27 y^3
Example 13. Find the cube of 2 xy.
Solution :( 2 xy)^3 ( 2 x)^3 3 ( 2 x)^2 y 3 2 xy^2 y^3
= 8 x^3 3 4 x^2 y 6 xy^2 y^3
= 8 x^3 12 x^2 y 6 xy^2 y^3
Activity : Find the cube with the help of the formulae.- 3 x 2 y 2. 3 x 4 y 3. 397
Example 14. If x 37 , what is the value of 8 x^3 72 x^2 216 x 216?
Solution : 8 x^3 72 x^2 216 x 216
= ( 2 x)^3 3 ( 2 x)^2 6 3 2 x.( 6 )^2 ( 6 )^3
= ( 2 x 6 )^3
= ( 2 u 37 6 )^3 [substituting the values]
= ( 74 6 )^3
= ( 80 )^3
= 512000
Example 15. If xy 8 and xy 5 , what is the value of x^3 y^3 8 (xy)^2?
Solution :x^3 y^3 8 (xy)^2
= (xy)^3 3 xy(xy) 8 {(xy)^2 4 xy}
= ( 8 )^3 3 u 5 u 8 8 ( 82 4 u 5 ) [substituting the values]
= 83 15 u 8 8 ( 64 20 )
= 83 15 u 8 8 u 84
= 8 ( 82 15 84 )
= 8 ( 64 15 84 )
= 8 u 163
= 1304