State true or false.

The value of $(0.013) 3 + (0.007) 3 (0.013) 2 − 0.013 × 0.013 × 0.007 + (0.007) 2$ will be 0.02.

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True

False

answer is A.

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Detailed Solution

We have to check if value of

(0.013) 3 + (0.007) 3 (0.013) 2 − 0.013 × 0.013 × 0.007 + (0.007) 2

will be 0.02.
Using the identity,

a 3 + b 3 = (a + b) (a 2 − a b + b 2)

= (0.013 + 0.007) ((0.013) 2 − 0.013 × 0.007 + (0.007) 2) (0.013) 2 − 0.013 × 0.007 + (0.007) 2

..........(1)
Evaluating (1) and canceling

((0.013) 2 − 0.013 × 0.007 + (0.007) 2)

both in the numerator and the denominator,
=0.013+0.007
=0.020
=0.02
So, the value of

(0.013) 3 + (0.007) 3 (0.013) 2 − 0.013 × 0.013 × 0.007 + (0.007) 2

will be 0.02.
Thus, the given statement is true.
Therefore, option 1 is correct.

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