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# Without actually calculating the cubes, find the value of each of the following:

i) (-12)³ + (7)³ + (5)³

ii) (28)³ + (-15)³ + (-13)³

**Solution:**

i) (-12)³ + (7)³ + (5)³

Let x = -12, y = 7, z = 5

Then x + y + z = -12 + 7 + 5 = 0

We know the algebraic identity, if x + y + z = 0 then x³ + y³ + z³ = 3xyz

Thus, (-12)³ + (7)³ + (5)³ = 3(-12)(7)(5)

= -1260

ii) (28)³ + (-15)³ + (-13)³

Let x = 28, y = -15, z = -13

Then x + y + z = 28 - 15 - 13 = 0

We know the algebraic identity, if x + y + z = 0 then x³ + y³ + z³ = 3xyz

Thus, (28)³ + (-15)³ + (-13)³ = 3(28)(-15)(-13)

= 16380

**☛ Check: **Class 9 NCERT Solutions Maths Chapter 2

**Video Solution:**

## Without actually calculating the cubes, find the value of each of the following: i) (-12)³ + (7)³ + (5)³ ii) (28)³ + (-15)³ + (-13)³

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 14

**Summary:**

The value of each of the following (−12)³ + (7)³ + (5)³ and (28)³ + (−15)³ + (−13)³ without actually calculating the cubes are -1260 and 16380 respectively.

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