Practice Algebraic Identities Practice Questions with Detailed Solutions – Level 2

If \(x + \dfrac{1}{x} = 5,\) what is the value of \(x^{3} + \dfrac{1}{x^{3}}?\)

If \(a\) and \(b\) are positive numbers such that \(a - b = 4\) and \(ab = 21,\) what is the value of \(a + b?\)

What is the value of \( \frac{387^3 + 113^3}{387^2 - 387 \times 113 + 113^2} \)?

If \(a - b = 3\) and \(ab = 10,\) what is the value of \(a^{3} - b^{3}?\)

If \(a^{2} + b^{2} + c^{2} = 50\) and \(ab + bc + ca = 47,\) what is the value of \(a + b + c,\) given that \(a + b + c\) is positive?

If \(a + b + c = 9\) and \(ab + bc + ca = 23,\) what is the value of \(a^{3} + b^{3} + c^{3} - 3abc?\)

What is the value of \(103^{3}\) \({}- 3\) \({}\times 103^{2}\) \({}\times 3\) \({}+ 3\) \({}\times 103\) \({}\times 9\) \({}- 27?\)

If \(x - \dfrac{1}{x} = 4,\) what is the value of \(x^{4} + \dfrac{1}{x^{4}}?\)

If \(a + b = 7\) and \(a^{2} + b^{2} = 29,\) what is the value of \(a^{3} + b^{3}?\)

If \(a + b + c = 15\) and \(a^{2} + b^{2} + c^{2} = 83,\) what is the value of \(ab + bc + ca?\)