What is the simplified value of
(0.04)
3
+(0.21)
3

(0.04)
2
+(0.21)
2
−0.0084
​
?

Let a=0.04 and b=0.21.
Note that a×b=0.04×0.21=0.0084.

The given expression can be written in terms of a and b as:

a
3
+b
3

a
2
+b
2
−ab
​

We know the algebraic identity for the sum of cubes:

a
3
+b
3
=(a+b)(a
2
−ab+b
2
)
Substituting this into the expression:

(a+b)(a
2
−ab+b
2
)
a
2
+b
2
−ab
​
=
a+b
1
​

Substitute back the values of a and b:

=
0.04+0.21
1
​
=
0.25
1
​