Difference of Squares & Perfect Square Trinomials

The difference of squares formula states that $$a^2 - b^2 = (a - b)(a + b)$$ .

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, such as $$a^2 + 2ab + b^2 = (a + b)^2$$ .

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

The GCF of 18 and 36 is 18.

No, because $$x^3$$ is not a perfect square.

$$x^2 - 10x + 20$$ is NOT a perfect square trinomial.

$$3(x + 5)(x - 5)$$ .

No, $$x^2 + 81$$ is prime.

The formula is $$a^2 + 2ab + b^2 = (a + b)^2$$ or $$a^2 - 2ab + b^2 = (a - b)^2$$ .

The first step is to find the GCF (Greatest Common Factor) of all the terms.