Find the following products: `(0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+0. 49 y^2)`
`((2x)/5-(3y)/7)((9y^2)/(49)+(4x^2)/(25)+(6x y)/(35))`

Explanation

Given
`(i)``(0. 9 x+0. 7 y)(0. 81 x^2-0. 63x y +0. 49 y^2)`
`=(0. 9 x+0. 7 y)(0. 9 x)^2 - (0. 9 x)(0. 7 y) + (0. 7 y)^2`
Using identity
`a^3+b^3=(a+b)(a^2 -ab+b^2)`
`=(0.9x)^3 +(0.7y)^3`
`=0.729x^3+0.343y^3`
`(ii)``((2x)/5-(3y)/7)((9y^2)/(49)+(4x^2)/(25)+(6x y)/(35))`
Using identity
`a^3-b^3=(a-b)(a^2 +b^2+ab)`
`[((2x)/5-(3y)/7)((3y)/(7))^2+((2x)/(5))^2+(3y/7) xx (2x/5)]`
`((2x)/(5))^3-(3y/7)^3`
`=((8x^3)/125)) - ((27y^3)/343))`
Hence the answers are
`=0.729x^3+0.343y^3` and `(8x^3)/(125) - (27y^3)/(343)`