Square of Binomial Patterns

Factoring Special Patterns

By Kim Spurling

​First - Let's review what a perfect square is:

​A perfect square is: an integer (such as 9 or 36) whose square root is an integer.

​

Other examples: 4, 16, 64, 81. 100​

​

​First Special Case:

Factoring the Difference of Squares

​a² - b² = (a - b)(a + b)

​

Ex.) x² - 64 = (x - 8)(x + 8)​

Multiple Choice

Factor a² - 36

• (a + 6)(a + 6)

• (a - 6) (a - 6)

• (a + 6) (a - 6)

• prime

Poll

Why is the factored answer of the following problem incorrect?

x² - 81 = (x + 9)(x + 9)

• Because both factors should be (x-9)

• Because 9 $$\cdot$$  9 $$\ne$$  81

• Since there is a minus sign, the factors must be (x+9)(x-9)

• It is correct

Multiple Choice

What is a polynomial with three terms called?

• Monomial

• Binomial

• Trinomial

• Polynomial

​Second Special Case:

​Factoring Perfect Square Trinomials