Express 2−23+22\displaystyle \frac{2 - \sqrt{2}}{3 + 2\sqrt{2}}3+222−2 in the form a+b2a + b\sqrt{2}a+b2, where a a\,a and b b\,b are integers.
233 exam-style questions on Edexcel A Level Maths Algebraic Expressions, covering 1.1 Index Laws, 1.2 Expanding Brackets, 1.3 Factorising, 1.4 Negative and Fractional Indices, and 1.5 Surds. Each one has a worked solution and a mark scheme showing where the marks go.