Question

14. Without actually calculating the cubes, find the value of each of the following:
(1) (-12) + (7) +(5)3
(ii) (28)+(-15) + (-13)3
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Answer 1

Answer:

1. 120

2. - 2184

Step-by-step explanation:

PLEASE MARK AS BRAINLIEST???

Answer 2

Answer:

i) -1260

ii) 16380

Step-by-step explanation:

(i) (-12)³ + (7)³ + (5)³

We know that

x³ + y³ + z³ - 3xyz = (x + y + z) (x² + y² + z² - xy - yz - zx)

So, x³ + y³ +z³ = 3xyz + (x + y + z) (x² +y² + z² - xy - yz - zx)

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

(-12)³ + (7)³ + (5)³

= 3 (-12) (7) (5)

+ ( -12 + 7 + 5) ( (-12)² + (7)²+ (5)² - (-12) (7) - (7) (5) - (5) (-12) )

= 3 (-12) (7) (5) + (0) ( (-12)² + (7)² + (5)²- (-12) (7) - (7) (5) - (5) (-12)

= 3 (-12) (7) (5)

= -1260

(ii) (28)³ + (-15)³ + (-13)³

We know that

x³ + y³ + z³ - 3xyz = (x + y + z) (x² + y² + z² – xy – yz - zx)

So, x³ + y³ + z³ = 3xyz + (x + y + z) (x² + y² + z² - xy - yz - zx)

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

(28)³ + (-15)³ + (-13)³

= 3 (28) (-15) (-13)

+ (28 - 15 -13) ( (28)² + (-15)² + (-13)² + (28) (-15) + (-15) (-13) + (-13) (28) )

= 3 (28) (-15) (-13) + 0

= 16380

hope this helps,

please mark brainliest, thanks!