If X = 110, Y = 111, Z = 112, then find the value of x³ + Y³ + Z³ - 3xyz.

If (a − 2b) = 8 and 2ab = 9, then find the value of (a + 2b).

If (a + b + c) = 20, a² + b² + c² = 152, find the value of a³ + b³ + c³ - 3abc

If x + y + z = 9, x² + y² + z² = 57 and xyz = -12, then the value of x³ + y³ + z³ is:

If a + b = c then find the value of (a + b - c)³ + 3abc.

If a = 53 and b = 13. Find the value of (a + b)² - (a - b)².

If (a + b + c) = 48, (a - b) = 4 , (b - c) = 6, (c - a) = 5 and (a³ + b³ + c³) = 2478 then, find the value abc/3.

If A +  B = - 5 and AB = 6, then find the value of A³ + B³

x = (a - b), y = (b - c), z = (c + a) and (ab + bc + ca) = 8. Find x² + y² - z².

If a + b + c = 0, then find the value of \(\frac{a^2+b^2+c^2}{a^2-bc}\)

If p + q = 12 and pq = 14, then find the value of p² - pq + q².

If 3x + 2y = 10 and 2xy = 7, then find the value of 3x - 2y. (if 3x - 2y > 0)

If a + b + c = 7, and a³ + b³ + c³ - 3abc = 7, then find the value of (ab + bc + ca).

a + b = 8, and ab = 6. What is the value of a³ + b³? 

If a + b = 10 and a² + b² = 58, find the value of ab.

If x + 3y = 6, what is the value of x³ + 27y³ + 54xy?

If x = y - z then find the value of \(x^3-y^3+z^3\).

If (a + b + c) = 12, and (ab + bc + ca) = 47, find the value of (a³ + b³ + c³ - 3 abc).

If x + y = 7 and xy = 19, then calculate the value of x² + y².

If p + q = 12 and pq = 14, then find the value of p² - pq + q².

If a + b + c = 5 and ab + bc + ca = 7, then the value of a³ + b³ + c³ - 3abc is :

If a + b + c = 10 and ab + bc + ca = 30, then the value of a² + b² + c² is:

If a + b = 11 and ab = 35, then what is the value of (a⁴ + b⁴)?

If x - y = 25 and xy = 444, compute the value of x³ – y³.

If x + y = 36, then find (x − 27)³ + (y − 9)³.

If 2x + 3y = 9, and xy = 3, what is 8x³ + 27y³?

If p + q +r = 0, then what is the simplified value of the expression ( \(\frac{p^2}{p^2 - qr} + \frac{q^2}{q^2 - pr} + \frac{r^2}{r^2 - pq}\) )

If X = 110, Y = 111, Z = 112, then find the value of x³ + Y³ + Z³ - 3xyz.

If a = 2022, b = 2021 and c = 2020, then value of a² + b² + c² – ab – bc – ca is:

If x + y + z = 10 and xy + yz + zx = 15, then find the value of x³ + y³ + z³ - 3xyz

If x - 2y = 3 and 2xy = 5, then find the value of (x + 2y)².

If [√(a² + b² + ab)] + [√(a² + b² – ab)] = 1, then what is the value of (1 – a² )(1 – b² )?

If y² + 9x² = 12 and yx = 6 then, find the value of (y + 3x)³/\(4\sqrt3\).

If a⁶ + b⁶ – c⁶ + 2a³b³ – 9a²b²c² + 6abc⁴ = 0, then what is the value of |(a + b)/c|?

If x + y = 10 and xy = 12, find the value of x² - xy + y² .

If (a + b)² = 196 and ab = 12, then find the value of 2(a³ + b³). 

If x + y + z = 3, x² + y² + z² = 45 and x³ + y³ + z³ = 69, then what is the value of xyz ?

If l + m  + n = 0, then what will be the value of \((\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})\) ?
 

If (a - b) = 9, and (a³ - b³) = 4401, find the value of ab.

If (a + b + c) ≠ 0, then (a + b + c) (a² + b² + c² - ab - bc - ca) is equal to: 

If x² - 2xy = 84 and x - y = -10, then the value of y is:

If (a − 2b) = 8 and 2ab = 9, then find the value of (a + 2b).

If (a + b + c) = 19, and (a² + b² + c²) = 155, find the value of (a - b)² + (b - c)² + (c - a)².

If a + b + c = 0, then find the value of \(\frac{a^2+b^2+c^2}{a^2-bc}\)

If 4a + 9b = 3 and ab = -3, then find the value of (16a² + 81b²).

If (a³ + b³ + c³ - 3abc) = 405, and (a + b + c) = 15, find the value of (a - b)² + (b - c)² + (c - a)².

If a – b = 2 and a³ – b³ = 80, then what will be the value of ab?

If 2a + 3b = 14 and 2a - 3b = 10, then find the value of 'ab'.

If (a² + b² + c²) = 64 , (ab + bc + ca) = 256 and abc = 987 then, find the value of (a³ + b³ + c³).

x = (a - b), y = (b - c), z = (c + a) and (ab + bc + ca) = 8. Find x² + y² - z².