Factoring Difference of Squares and Perfect Square Trinomials

The difference of squares formula states that for any two numbers a and b, $$a^2 - b^2 = (a - b)(a + b)$$ .

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as $$a^2 + 2ab + b^2 = (a + b)^2$$ or $$a^2 - 2ab + b^2 = (a - b)^2$$ .

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

$$x^2 + 10x + 25 = (x + 5)^2$$ .

$$25x^2 - 70x + 49 = (5x - 7)^2$$ .

An expression is 'not factorable' if it cannot be expressed as a product of two or more factors using real numbers.

$$n^2 + 10n + 25 = (n + 5)^2$$ .

$$x^2 - 9 = (x + 3)(x - 3)$$ .

Identify the two squares in the expression and apply the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$ .

Check if the trinomial can be expressed as $$a^2 + 2ab + b^2$$ or $$a^2 - 2ab + b^2$$ and then factor accordingly.