Question

Using suitable identity, prove that
(0.87)^3 + (0.13)^3 / (0.87)^2 -(0.87*0.13) + (0.13)^2

Answer 1

a^3 + b^3 = (a + b) * (a^2 - ab + b^2) 

That's the factoring for the sum of 2 cubes. 

So: 

(0.87^3 + 0.13^3) / (0.87^2 - 0.87 * 0.13 + 0.13^2) => 
(0.87 + 0.13) * (0.87^2 - 0.87 * 0.13 + 0.13^2) / (0.87^2 - 0.87 * 0.13 + 0.13^2) 
Simplify: 
0.87 + 0.13 => 
1.00 => 
1