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Understanding Special Factoring Techniques: Difference of Two Squares and Perfect Square Trinomials

This section focuses on two special factoring techniques: the Difference of Two Squares and Perfect Square Trinomials. The Difference of Two Squares can be identified when both terms are perfect squares with a subtraction sign in between. Examples include x² – 36 and 100 – t². Perfect Square Trinomials can be recognized when both the first and last terms are perfect squares, and the last sign is positive, such as a² + 2ab + b². Always remember to check for a Greatest Common Factor (GCF) first before using other factoring methods.

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Understanding Special Factoring Techniques: Difference of Two Squares and Perfect Square Trinomials

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  1. MTH 092 Section 11.5 Special Factoring Techniques

  2. The Difference of Two Squares • How to recognize one: • The first term is a perfect square (1, 4, 9, 16, 25, 36, etc., or a variable with an even exponent) • The last term is a perfect square. • There is a subtraction sign between the terms.

  3. Examples • x2 – 36 • 100 – t2 • 36y2 – 25 • n4 – 16 • 49y2 + 1

  4. Perfect Square Trinomials • It MAY be a perfect square trinomial: • The first term is a perfect square. • The last term is a perfect square. • 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)

  5. Examples • x2 + 22x + 121 • p2 – 4p + 4 • n2 – 18n – 144 • 25a2 – 40ab + 16b2 • y2 + 4y + 16

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

  7. Examples • 2n2 – 28n + 98 • -9t2 + 1 • 36x2 – 64y2 • y3 + 12y2 + 36y

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