Expanding, simplifying, factorising, and solving equations assorted problems

A set of assorted problems on expanding, simplifying, factorising, solving, requiring a knowledge of the following:

• A1a – Using and interpreting algebraic notation
• A4a – Simplifying and manipulating algebraic expressions by collecting like terms (basic)
• A4b – Multiplying a single term over a bracket
• A4c – Factorising (basic)
• A4d – Multiplying two or more brackets
• A17b – Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation
• A18a – Solving quadratic equations by factorising