Algebraic manipulation

1. Simplify algebraic expressions by combining like terms, ensuring the result is in its simplest form, for example, transforming 2a + 3ab - 1 + 5a - 9ab + 4 into 7a - 6ab + 3. 2. Expand products of algebraic expressions, such as 3x(2x - 4y) and (3x + y)(x - 4y), including cases with more than two brackets like (x - 2)(x + 3)(2x + 1). 3. Factor expressions by taking out common factors, fully factorising them, for instance, converting 9x + 15xy into 3x(3x + 5y). 4. Factor expressions of specific forms, including: • ax + bx + kay + kby • ax - by • a + 2ab + b • ax + bx + c • ax + bx + cx. 5. Complete the square for expressions structured as ax² + bx + c.