How do you factor (x^2-5)(x25)?

1 Answer
Oct 29, 2015

x^2-5 = (x-sqrt(5))(x+sqrt(5))x25=(x5)(x+5)

Explanation:

The difference of squares identity can be written:

a^2-b^2=(a-b)(a+b)a2b2=(ab)(a+b)

In order to treat x^2-5x25 as a difference of squares, we need to recognise that 5 = (sqrt(5))^25=(5)2, then we find:

x^2-5 = x^2-(sqrt(5)^2) = (x-sqrt(5))(x+sqrt(5))x25=x2(52)=(x5)(x+5)

In other words, we let a=xa=x and b=sqrt(5)b=5