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

If 2x + 3y = 9, and xy = 3, then find the value of 8x³ + 27y³.

If x^1/3 + y^1/3 - z^1/3 = 0, then find the value of (x + y - z)³ + 27 xyz.

If (a + b) = 7 and ab = 3, then what is the value of (a³ + b³)?

If a + b + c = 12 and ab + bc + ca = 40, then what is the value of a² + b² + c² ?

If a = 3 and b = -5 then find the value of 11a³ - 2b³ + 5a²b - 8ab².

If (a + b) = 17 and ab = 72, then find the value of a³ + b³.

If x³ + y³ = 88 and x + y = 4 then what would be the value of xy, where x and y are the real numbers?

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

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

If (a² + b² + c²) = 70 and (ab + bc + ca) = 63. What is the value of \({\sqrt9(a+b+c)^2}\over (ab+bc+ca)\)? 

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

Find the value of a³ + b³ + c³ – 3abc, if a + b + c = 14, a² + b² + c² = 156.

If , (a + b)³ + (a − b)³ = 2a[Ma² + Nb²] . Then Find √(M + N)

If a + b + c = 12 and ab + bc + ca = 40, then what is the value of a² + b² + c² ?

If a = 2.3 and b = 0.7, find the value of 9a² + 12ab + 4b². 

If a² + b² = 17, find the value of (a + b)² + (a - b)².

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

If x³ – y³ = 456 and x – y = 6. Find the value of (x + y)² – xy.

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

If a² - b² = 72 & ab = 27, find \(\frac{b}{a} - \frac{a}{b}\).

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

If (a + b + c) = 20 and a² + b² + c² = 262 then, find the value of ab+ bc + ca

If 8a³ + 27b³ = 16 and 2a + 3b = 4,then find the value of 16a⁴ + 81b⁴ .

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

If x^1/3 + y^1/3 - z^1/3 = 0, then find the value of (x + y - z)³ + 27 xyz.

If x + y + z = 11, xy + yz +zx = - 6, and  x³ + y³ + z³ = 1604, then find the value of xyz is:

If 2x + 5y = 15 and xy = 6, then the value of 4x² + 25y² is ____________.

If a + 2b + 3c = 0, then what is the value of (a³ + 8b³ + 27c³ )?

If a - b = 3 and a³ - b³ = 999, then Find the value of a² - b².

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

If 4x² + y² = 40 and xy = 6, then find the value of 2x + y.

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

If a² + b² + 49c² + 18 = 2(b - 28c - a), then the value of (a - b - 7c) is:

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

If (a + b + c) = 16, and (a² + b² + c²) = 90, find the value of (ab + bc + ca).

If a + b + c =7, ab + bc + ca = 11 and abc = -1, then a³ + b³+ c³ is equal to:

The expansion of (3a - 4b - 2c)² is:

If x + y = 16 then what is the maximum value of xy?

If a² + b² = 17, find the value of (a + b)² + (a - b)².

If a + b + c = 6 and a² + b² + c² = 14, then what is the value of (a - b)² + (b − c)² + (c- a)²?

If (a + b) = 17 and ab = 72, then find the value of a³ + b³.

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.

Find the value of a + b + c, if a, b, and c are the three factors of x³– 7x – 6.

 What must be subtracted from x³ - 3x²y + 3xy² - y³ to get x³ - y³?

 If a² + 2(b - 1) (c - 1) = 73, b² + 2(c - 1)(a - 1) = 75.5, c² + 2(a - 1) (b - 1) = 78.5 then find a+b+c  where  a, b, c are positive numbers?

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 a² + b² + 49c² + 18 = 2(b - 28c - a), then the value of (a - b - 7c) is:

Solve the given set of three equations to get the value of the unknowns:

x + 2z = 3

x + 2y + 3z = 5

3x - 5z = -13