Home
Class 9
MATHS
Without actually calculating the cubes,...

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`

Text Solution

AI Generated Solution

To solve the given problems without calculating the cubes directly, we can use the algebraic identity for the sum of cubes. The identity states: \[ x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) \] If \(x + y + z = 0\), then we have: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the value of each of the following: (i) (-3)^2 (ii) (-4)^3 (iii) (-5)^4

Find the value of each of the following: (i) 13^2 (ii) 7^3 (iii) 3^4

Find the value of each of the following: (i) (-7)^2 (ii) (-3)^4 (iii) (-5)^5

Without actually calculating the cube find the value of the following : (i) (-9)^(3)+(4)^(3)+(5)^(3) " " (ii) (-18)^(3)+(9)^(3)+(9)^(3) " " (iii) (16)^(3)+(1)^(3)+(-17)^(3) (iv) (8)^(3)+(3)^(3)+(-11)^(3) .

i) (1.2)^3 ii) (3.5)^3

Evaluate each of the following (i) ((11)/(12))^3 (ii) (3/4)^(-3)

Without actually calculating the cube: (-12)^3+7^3+5^3

Find the value of n in each of the following: (i) 5^(2n)xx5^3=5^(11) (ii) 9xx3^n=3^7

Evaluate each of the following: (i) 111^3-\ 89^3 (ii) 46^3+34^3

without actually calculating , the cubes , find the valuse of (i) ((1)/(2))^(3)+((1)/(3))^(3)-((5)/(6))^(3) (ii) (0.2)^(3)-(0.3)^(3)+(0.1)^(3)