11. If a - b = 4 and a3 - b3 = 88, then find the value of a2 - b2.
12. If x3 + y3 + z3 = 3(1 + xyz), P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P3 + Q3 + R3 - 3PQR?
13. If ab(a + b) = 1, then what is the value of $$\frac{1}{{{a^3}{b^3}}} - {a^3} - {b^3}?$$
14. ab(a - b) + bc(b - c) + ca(c - a) is equal to:
15. If $$\frac{{a + b}}{c} = \frac{6}{5}$$ and $$\frac{{b + c}}{a} = \frac{9}{2},$$ then what is the value of $$\frac{{a + c}}{b}?$$
16. Simplify $$\frac{{{x^2} + 2x + {y^2}}}{{{x^3} - 5{x^2}}}{\text{if }}x + \frac{{{y^2}}}{x} = 5.$$
17. If a - b = 18 and a3 - b3 = 324, then find the value of ab.
18. If x - y = 3, then what is the value of x3 - y3 - 9xy?
19. What is the simplified value of $$\left( {x + \frac{1}{x}} \right)\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^4} + \frac{1}{{{x^4}}}} \right)\left( {{x^8} + \frac{1}{{{x^8}}}} \right)\left( {{x^{16}} + \frac{1}{{{x^{16}}}}} \right){\text{is:}}$$
20. If $${\text{A}} = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.2} \right)}^3} + {{\left( {0.3} \right)}^3} + 3\left( {0.005 + 0.016 + 0.027} \right) + 0.036}}{{{{\left( {0.1} \right)}^2} + {{\left( {0.2} \right)}^2} + {{\left( {0.3} \right)}^2} + 0.04 + 0.06 + 0.12}}$$ then the value of 60A is:
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