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 x = 3y + 4, then what is the value of (x³ - 27y³ - 36 xy)?

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

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

The algebraic expression 4x² - y² + 6y - 9 is equal to equal to______.

If x + y = 14, then the value of x³ + y³ + 42xy is:

If \(2a-b=3\) and \(8a^3-b^3=999 \), then the value of \(4a^2-b^2\).

If a³ + b³ + c³ - 3abc = 250 and a + b + c = 10, then what is the value of ab + bc + ca?

If ( a + b + c ) = 17 and ( a² +b² + c² ) = 117, what is the value of \(( a- b )^2 + (b - c )^2 + (c - a )^2 ?\)

If a + b + c = 7 and a³ + b³ + c³ - 3abc = 301, then ab + bc + ca = ?

If x + y + z = 10 and x² + y² + z²  =80 then what is the value of 4xy + 4yz + 4zx?

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

If a - b = 10 and ab = 4, then the value of a³ - b³ + 4(a + b)² is:

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

If 3^a = 27^b = 81^c and abc = 144, then the value of \(12\left(\frac{1}{a}+\frac{1}{2b}+\frac{1}{5c}\right)\) is

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 - c = 5 and ab - bc - ac = 10, then find the value of a² + b² + c².

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

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

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

Find the value of (a³ + b³+ c³ - 3abc), where a = 335, b= 215 and c = 180.

Simplify the following expression. \(\frac{(a^2+b^2-c^2)^2- (a^2-b^2+c^2)^2}{b^2-c^2}\)

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

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

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

If x³ = 270 + y³ and x = (6 + y), then what is the value of (x + y)? (given that x > 0 and y > 0)

If x = 3y + 4, then what is the value of (x³ - 27y³ - 36 xy)?

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

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

If 2x + 3y = 4 and 4x² + 9y² = 64, then what is the value of 8x³ + 27y³.

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 (x - y) = 6, (y - z) = 10 and (z - x) = 2, find the value of 2 × [(a³ + b³ + c³ - 3abc)/(a + b + c)].

If a = 66, b = 68, c = 65, find the value of a³ + b³ + c³ - 3abc. 

If (a + b + c) = 14, and (a³ + b³ + c³ - 3abc) = 98, find the value of (a² + b² + c²).

If a² + b² = 105 and a + b = 11, what would be the value of ab?

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

If (x + y + z) = 3a then find the value of the expression (a – x)³ + (a – y)³ + (a – z)³.

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

If a² + b² + ab = 71 and a - b = 2, then find the value of a³ - b³.

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.

If (ab + bc + ca) = 18 and (a + b + c) = 15, find the value of (a² + b² + c²).

Simplify the given equation: \({(a - b)^3 - (a + b)^3}\over {b^2 + 3a^2}\)

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

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

If 3x - y = 12, xy = 15, then find the value of {x³ - (y³/27)}

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

If 25a² + b² = 60, ab = 4, where a, b > 0 then, find the value of \(\sqrt{125a^3+b^3}\).