Difference of Two Squares Flashcards

All 4 cards in this deck

What is the factorisation of $a^2 - b^2$?

$(a - b)(a + b)$

True or false? $x^2 + 9$ factorises as $(x + 3)(x + 3)$.

False. A sum of two squares does not factorise; only a difference of two squares does.

How do you factorise a difference of two squares when the squared term has a coefficient?

e.g. $9x^2 - 25$

Use the square root of each term in the brackets.

Here: $(3x - 5)(3x + 5)$

What are the steps to factorise fully a difference of two squares that has a common factor?

e.g. $50 - 2y^2$

1. Take out the common factor: $2(25 - y^2)$
2. Square root each term in the bracket: $5$ and $y$
3. Write as two brackets: $2(5 + y)(5 - y)$