Answer:
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(0) 2b + 5(11) ax - by
The cubes of (0) 2b + 5(11) ax - by are:
* 2b: 2b x 2b x 2b = 8b^3
* 5(11) ax: 5(11) x 11 = 55, so 5(11) ax = 55ax
* -by: -by x -by x -by = -b^3y^3
Therefore, the cubes of (0) 2b + 5(11) ax - by are 8b^3 - 55ax - b^3y^3.
(ii) a ^ 2 - b ^ 2
The cube of a ^ 2 - b ^ 2 is:
* a^2: a x a x a = a^3
* -b^2: -b x -b x -b = -b^3
Therefore, the cube of a ^ 2 - b ^ 2 is a^3 - b^3.
(iv) - 7a + 2b ^ 26
The cube of - 7a + 2b ^ 26 is:
* -7a: -7a x -7a x -7a = -49a^3
* 2b^26: 2b x 2b x 2b x ... x 2b (26 times) = 2b^26
Therefore, the cube of - 7a + 2b ^ 26 is -49a^3 + 2b^26.
(v) 2a - 3bc
The cube of 2a - 3bc is:
* 2a: 2a x 2a x 2a = 8a^3
* -3bc: -3bc x -3bc x -3bc = -9b^2c^2
Therefore, the cube of 2a - 3bc is 8a^3 - 9b^2c^2.
(vi) 1 + a - 2b
The cube of 1 + a - 2b is:
* 1: 1 x 1 x 1 = 1
* a: a x a x a = a^3
* -2b: -2b x -2b x -2b = -4b^3
Therefore, the cube of 1 + a - 2b is 1 + a^3 - 4b^3.
(vii) 42
The cube of 42 is:
* 42: 42 x 42 x 42 = 1764
Therefore, the cube of 42 is 1764.
(viii) a - 2b - 3c
The cube of a - 2b - 3c is:
* a: a x a x a = a^3
* -2b: -2b x -2b x -2b = -4b^3
* -3c: -3c x -3c x -3c = -9c^3
Therefore, the cube of a - 2b - 3c is a^3 - 4b^3 - 9c^3.
(ix) x ^ 2 - y - z
The cube of x ^ 2 - y - z is:
* x^2: x x x x = x^4
* -y: -y x -y x -y = -y^3
* -z: -z x -z x -z = -z^3
Therefore, the cube of x ^ 2 - y - z is x^4 - y^3 - z^3.
(x) 105(1x) p ^ 2 - q ^ 2 - r ^ 2
The cube of 105(1x) p ^ 2 - q ^ 2 - r ^ 2 is:
* 105: 105 x 105 x 105 = 11225
* p^2: p x p x p = p^3
* q^2: q x q x q = q^3
* r^2: r x r x r = r^3
Therefore, the cube of 105(1x) p ^ 2 - q ^ 2 - r ^ 2 is 11225 - 3p^3 - 3q^3 - 3r^3.
(xi) 999
The cube of 999 is:
* 999: 999 x 999 x 999 = 999001
Therefore, the cube of 999 is 999001.
Explanation: