The value of (0.03)\(^3\) - (0.02)\(^3\) is
A
0.019
B
0.0019
C
0.00019
D
0.000019
E
0.000035
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Using the method of difference of two cubes,
\(a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})\)
\((0.03)^{3} - (0.02)^{3} = (0.03 - 0.02)((0.03)^{2} + (0.03)(0.02) + (0.02)^{2}\)
= \((0.01)(0.0009 + 0.0006 + 0.0004)\)
= \(0.01 \times 0.0019\)
= \(0.000019\)
Source: Myschool Past Questions Archive (Record #32454)