Factoring Difference of Squares and Perfect Square Trinomials

What is the difference of squares formula?

• a^2 - b^2 = (a + b)(a - b)

• a^2 + b^2 = (a + b)(a - b)

• a^2 - b^2 = (a + b)^2

• a^2 + b^2 = (a - b)^2

Factor the expression: x^2 + 6x + 9

• (x + 3)^2

• (x + 2)(x + 4)

• (x + 1)(x + 5)

• (x + 3)(x + 3)

What is the first step in factoring a difference of squares?

• Identify the two perfect squares in the expression.

• Multiply the two terms together.

• Add the two terms together.

• Subtract the two terms from each other.

Factor the expression: x^2 - 9

• (x + 3)(x - 3)

• (x + 9)(x - 1)

• (x - 3)(x - 3)

• (x + 1)(x - 1)

Can the expression 9n^2 + 1 be factored using the difference of squares?

• Yes, it can be factored using the difference of squares.

• No, it cannot be factored using the difference of squares.

• It can be factored but not using the difference of squares.

• It can be factored using the sum of squares.

What is a perfect square trinomial?

• A trinomial that can be expressed as the square of a binomial, e.g., a^2 + 2ab + b^2 = (a + b)^2.

• A polynomial that has three terms and is always positive.

• A trinomial that can be factored into two linear factors with real coefficients.

• A quadratic equation that has no real solutions.

Factor the expression: x^2 - 16

• (x + 4)(x - 4)

• (x + 8)(x - 2)

• (x - 4)(x - 4)

• (x + 2)(x + 8)

Is x^2 + 14x + 49 a perfect square trinomial?

• Yes, it is.

• No, it is not.

• It could be, depending on the values of x.

• Only if x is a whole number.

Factor the expression: 25x^2 + 60x + 36

• (5x + 6)^2

• (5x + 6)(5x - 6)

• (5x - 6)(5x - 6)

• (5x + 12)(5x - 3)

Can the expression x^2 + 1 be factored using the difference of squares?

• Yes, it can be factored using the difference of squares.

• No, it cannot be factored using the difference of squares.

• Yes, it can be factored as (x + 1)(x - 1).

• No, it can be factored using the sum of squares.