1. Factoring Special Cases
Skill 54

2. Objective
HSA-SSE.1.a: Interpret parts of an expression such as terms, factors, and coefficients.

3. 𝒂 𝟐 +𝟐𝒂𝒃+ 𝒃 𝟐 = 𝒂+𝒃 𝒂+𝒃 = 𝒂+𝒃 𝟐 𝒂 𝟐 −𝟐𝒂𝒃+ 𝒃 𝟐 = 𝒂−𝒃 𝒂−𝒃 = 𝒂−𝒃 𝟐
Special Cases
Perfect Square Trinomials
𝒂 𝟐 +𝟐𝒂𝒃+ 𝒃 𝟐
= 𝒂+𝒃 𝒂+𝒃
= 𝒂+𝒃 𝟐
𝒂 𝟐 −𝟐𝒂𝒃+ 𝒃 𝟐
= 𝒂−𝒃 𝒂−𝒃
= 𝒂−𝒃 𝟐
Difference of Squares
𝒂 𝟐 − 𝒃 𝟐
= 𝒂+𝒃 𝒂−𝒃

4. Example; Special Cases
Factor the perfect square trinomials.
𝟒𝟗 𝒙 𝟐 +𝟕𝟎𝒙+𝟏𝟎𝟎
= 7𝑥 𝑥
= 7𝑥+10 7𝑥+10
= 𝟕𝒙+𝟏𝟎 𝟐
𝒙 𝟐 −𝟐𝟐𝒙+𝟏𝟐𝟏
= 𝑥 2 −2 𝑥
= 𝑥−11 𝑥−11
= 𝒙−𝟏𝟏 𝟐

5. Example; Special Cases
Factor the difference of squares.
𝒙 𝟐 −𝟒𝟎𝟎
= 𝑥 2 −
= 𝒙+𝟐𝟎 𝒙−𝟐𝟎
𝟏𝟒𝟒 𝒙 𝟐 −𝟖𝟏
= 12𝑥 2 − 9 2
= 𝟏𝟐𝒙+𝟗 𝟏𝟐𝒙−𝟗

6. 54: Factoring Special Cases
Questions?
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