MTH 092

Section 11.5Special Factoring Techniques

The Difference of Two Squares

• How to recognize one:1.The first term is a perfect square (1, 4, 9, 16,

25, 36, etc., or a variable with an even exponent)

2.The last term is a perfect square.3.There is a subtraction sign between the terms.

bababa 22

Examples

• x2 – 36• 100 – t2

• 36y2 – 25• n4 – 16• 49y2 + 1

Perfect Square Trinomials

• It MAY be a perfect square trinomial:1. The first term is a perfect square.2. The last term is a perfect square.3. The last sign is positive.• a2 + 2ab + b2 = (a + b)2

• a2 – 2ab + b2 = (a – b)2

• Use FOIL to check. If it doesn’t work, try another factoring strategy (AC or Guess-and-Check)

Examples

• x2 + 22x + 121• p2 – 4p + 4• n2 – 18n – 144• 25a2 – 40ab + 16b2

• y2 + 4y + 16

Remember!!!

• Always look for a GCF before attempting other factoring strategies!

Examples

• 2n2 – 28n + 98• -9t2 + 1• 36x2 – 64y2

• y3 + 12y2 + 36y