Expanding & Factorising Flashcards

All 5 cards in this deck

What are the steps to expand and simplify a product of two brackets?

e.g. $(2x+3)(x-4)$

1. Multiply every term in the first bracket by every term in the second: $2x^2 - 8x + 3x - 12$
2. Collect like terms: $2x^2 - 5x - 12$

What are the steps to expand and simplify a product of three brackets?

e.g. $(x+1)(x+2)(x+3)$

1. Expand any two brackets: $(x+1)(x+2) = x^2+3x+2$
2. Multiply every term of that quadratic by each term of the remaining bracket: $x^3+3x^2+2x+3x^2+9x+6$
3. Collect like terms: $x^3+6x^2+11x+6$

What does "factorise fully" mean?

Take out the highest common factor of all the terms (numbers and letters), so the bracket has no common factor left.
e.g. $6x^2y + 21xy = 3xy(2x+7)$

What happens to the signs when you subtract a bracketed expression?

e.g. $\ldots - (3x^2 - 5x + 2)$

Every term inside the bracket changes sign.
e.g. it becomes $\ldots - 3x^2 + 5x - 2$

True or false? Leaving a term as $2x^3 \times 3x^2$ in an expansion is acceptable in the final answer.

False. Terms must be fully processed — it must be written as $6x^5$.