Verified answer

Answer:

To find the value of each expression without calculating the cubes explicitly, we can simplify the expressions using the properties of cubes.

(i) (-12) + (7)³ + (5)³:

The cube of a negative number remains negative, so we can rewrite the expression as:

(-12) + (-7³) + (5)³

Now, we can simplify the expression:

(-12) + (-7³) + (5)³

= -12 + (-343) + 125

= -12 - 343 + 125

= -355 + 125

= -230

Therefore, the value of (-12) + (7)³ + (5)³ is -230.

(ii) (28)³ + (-15)³ + (-13)³:

Similarly, the cube of a negative number remains negative, so we can rewrite the expression as:

(28)³ + (-15)³ + (-13)³

Now, we can simplify the expression:

(28)³ + (-15)³ + (-13)³

= 28³ + (-15³) + (-13³)

= 28³ - 15³ - 13³

Therefore, without calculating the cubes explicitly, the value of (28)³ + (-15)³ + (-13)³ cannot be determined.

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