Practice Algebraic Identities Practice Questions with Detailed Solutions – Level 1

If \(a + b = 10\) and \(ab = 21,\) what is the value of \(a^{2} + b^{2}?\)

If \(x - y = 4\) and \(xy = 12,\) find the value of \(x^{2} + y^{2}.\)

What is the value of \(87^{2} - 13^{2}?\)

If \(p + q = 5\) and \(pq = 6,\) what is the value of \(p^{3} + q^{3}?\)

If \(x - \frac{1}{x} = 3\), what is the value of \(x^3 - \frac{1}{x^3}\)?

If \(a + b + c = 9\) and \(ab + bc + ca = 26,\) find the value of \(a^{2} + b^{2} + c^{2}.\)

If \(a + b + c = 10\) and \(a^{2} + b^{2} + c^{2} = 40,\) what is the value of \(a^{3} + b^{3} + c^{3} - 3abc?\)

Simplify: \( \frac{2.3^3 + 1.7^3}{2.3^2 - 2.3 \times 1.7 + 1.7^2} \)

What is the value of \((47 + 23)^{2} - (47 - 23)^{2}?\)

If \(x + \frac{1}{x} = 6\), what is the value of \(x^2 + \frac{1}{x^2}\)?