Algebra MCQs

If x + y = √3 and x - y = √2, then the value of 8xy(x² + y²) is?

A = $$\frac{{{x^8} - 1}}{{{x^4} + 1}}$$  and B = $$\frac{{{y^4} - 1}}{{{y^2} + 1}}.$$  If x = 2 and y = 9, then what is the value of A² + 2AB + AB²?

Simplify the following expression:
$$\frac{{{{\left( {{a^2} - 4{b^2}} \right)}^3} + 64{{\left( {{b^2} - 4{c^2}} \right)}^3} + {{\left( {16{c^2} - {a^2}} \right)}^3}}}{{{{\left( {a - 2b} \right)}^3} + {{\left( {2b - 4c} \right)}^3} + {{\left( {4c - a} \right)}^3}}}$$

If $$a = 2 + \sqrt 3 {\text{,}}$$   then the value of $$\left( {{a^2} + \frac{1}{{{a^2}}}} \right) = \,?$$

If a³ + b³ = 218 and a + b = 2, then the value of $$1 - \sqrt {ab} $$  is:

If x = $$a + \frac{1}{a}$$  and y = $$a - \frac{1}{a}$$  then $$\sqrt {{x^4} + {y^4} - 2{x^2}{y^2}} $$    is equal to:

If $$\left( {\sqrt a + \sqrt b } \right)$$   = 15 and $$\left( {\sqrt a - \sqrt b } \right)$$   = 3, then the value of $$\frac{{\sqrt {ab} }}{4}$$  is?

The value of $$\frac{{{{\left( {4.6} \right)}^4} + {{\left( {5.4} \right)}^4} + {{\left( {24.84} \right)}^2}}}{{{{\left( {4.6} \right)}^2} + {{\left( {5.4} \right)}^2} + 24.84}}$$     is:

ab(a - b) + bc(b - c) + ca(c - a) is equal to: