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King Charles 1 Mathematics Knowledge Organiser Algebra Basics: Expanding and Factorising Double Brackets Expanding Factorising To expand double brackets, each term in one bracket needs to be multiplied by each term in the other bracket. Examples: 1) Expand and simplify (x + 3)(x + 4) An expression is quadratic if the highest power of x is 2. = x2 + 4x + 3x + 12 = x2 + 7x + 12 Factorising quadratic expressions of the type ax2 + bx + c, where a, b and c are integers. 2) Expand and simplify (2x + 1)(3x – 3) 2) Factorise x2 – 4x – 21 = (x + 3)(x – 7) We need two numbers that add together to make -4 and multiply together to make -21. These numbers must be +3 and -7. When a = 1, two brackets (x For example: )(x ) Add together Multiply together 1) Factorise x2 + 5x + 6 We need two numbers that add together to make +5 and multiply together to make +6. These numbers must be +3 and +2 and so these are the numbers that we put inside the brackets. The answer will be (x + 3)(x + 2). = 6x2 – 6x + 3x – 3 = 6x2 – 3x – 3 3) Expand and simplify (4x – 2)2 = (4x – 2)(4x – 2) 3) Factorise x2 – 49 = (x + 7)(x – 7) This is a special case where both terms are squares and they are separated by a minus sign. It is called the difference of two squares. To factorise, find the square root of each term, one bracket will have a minus and one a plus. = 16x2 – 8x – 8x + 4 = 16x2 – 16x + 4 Linked Prior Topics Multiplication, expanding and factorising single brackets, calculating with negatives Vocabulary Expanding, factorising, simplify, expression, term, factor, quadratic Linked Future Topics Solving quadratic equations, cubic equations, graphs of quadratic and cubic equations