Difference of Two Squares Flashcards

All 5 cards in this deck

What is meant by "the difference of two squares"?

An expression of the form $a^2 - b^2$ — one square subtracted from another.
e.g. $x^2 - 16$

What is the factorised form of $x^2 - a^2$?

e.g. $x^2 - 16$

$(x + a)(x - a)$
e.g. $x^2 - 16 = (x + 4)(x - 4)$

What are the steps to factorise a difference of two squares?

e.g. $x^2 - 49$

1. Check it is a square subtract a square: $x^2$ and $7^2$
2. Square root each term: $x$ and $7$
3. Write one $+$ bracket and one $-$ bracket: $(x + 7)(x - 7)$

True or false? $x^2 + 25$ factorises to $(x + 5)(x + 5)$.

False.
A sum of two squares does not factorise; only $x^2 - 25$ does, giving $(x + 5)(x - 5)$.

True or false? $x^2 - 36$ can be factorised even though it has no $x$ term.

True.
It is a difference of two squares: $(x + 6)(x - 6)$.