Difference of two squares
A special pattern: a squared number minus another squared number factorises into (a - b)(a + b).
Last updated
Analogy
Like cutting a square from a bigger square and rearranging the L-shape into a rectangle.
Example
49 is 7^2x^2 - 7^2= (x - 7)(x + 7)
In practice
It gives a mental shortcut: 51 x 49 = (50 + 1)(50 - 1) = 2,500 - 1 = 2,499.
Practice
Flashcards
- Factorise x^2 - 49.(x - 7)(x + 7).
Questions people ask
Why is there no middle term?
When you expand (x - 7)(x + 7), you get -7x and +7x. They cancel each other out. That leaves only x^2 - 49. So an expression with just a square minus a square, and nothing in the middle, is a difference of two squares.
Does it work for x^2 + 49?
No. A plus sign between two squares does not factorise using real numbers. The pattern needs a minus. So x^2 - 49 factorises, but x^2 + 49 stays as it is. Check the sign before you try. Brackets cannot make it, as no pair multiplies out to that.