Curriculum
Course: Mathematics — Second Preparatory
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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Factoring Special Cases

Mathematics — Second Preparatory

Factoring Special Cases

Worked examples

Worked examples

Comparison aspectMain ideaKeywords
Example 1Factor x² − 49Factor
Solution
  • This is a difference of two squares
  • because 49 = 7². So x² − 49 = (x − 7)(x + 7)
differencesquaresbecause
Example 2
  • Factor x² + 10x + 25
  • then find its value when x = 15
Factorthenfindvalue
Solution
  • The expression is a perfect square
  • so it equals (x + 5)². When x = 15
  • the value is (15 + 5)² = 20² = 400. Check with the original expression: 225 + 150 + 25 = 400
expressionperfectsquareequals
Example 3Factor 16x⁴ − 1 completelyFactor16x⁴completely
Solution
  • 16x⁴ − 1 = (4x² − 1)(4x² + 1) = (2x − 1)(2x + 1)(4x² + 1). The factoring stops here
  • because 4x² + 1 does not factor into real factors
16x⁴factoringstopshere
Example 4Find the value of 100² − 99² without a calculatorFindvalue100²without
Solution100² − 99² = (100 − 99)(100 + 99) = 1 × 199 = 199. Check: 10000 − 9801 = 199100²Check100009801
Comparison aspectMain ideaKeywords
Example 5Factor 25x² − 16y²Factor25x²16y²
Solution
  • This is a difference of two squares
  • because 25x² = (5x)² and 16y² = (4y)². So 25x² − 16y² = (5x − 4y)(5x + 4y). Check: 25x² + 20xy − 20xy − 16y² = 25x² − 16y²
differencesquaresbecause25x²
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