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Factoring Perfect Square Trinomials

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Factoring Perfect Square Trinomials

  1. 1. Grade 8 – Mathematics Quarter I FACTORING PERFECT SQUARE TRINOMIALS
  2. 2. Objectives: 1. identify whether or not an expression is a perfect square trinomial; and 2. factor perfect square trinomials completely.
  3. 3. Tell whether the following expression is a perfect square trinomial or not. 1. 𝑥2 + 2xy + 𝑦2 2. 4𝑥2 + 20x + 25 3. 𝑥2 + 5x + 6 4. 9𝑥2 + 30xy + 25𝑦2 5. 4𝑥2 + 2xy + 𝑦2 PERFECT SQUARE TRINOMIAL PERFECT SQUARE TRINOMIAL NOT NOT PERFECT SQUARE TRINOMIAL
  4. 4. PERFECT SQUARE TRINOMIAL 1. 𝑥2 + 2xy + 𝑦2 ( )2 + 2( )( ) + ( )2 2. 4𝑥2 + 20x + 25 ( )2 + 2( )( ) + ( )2 x yx y 2x 52x 5 FIRST TERM PERFECT SQUARE MIDDLE TERM TWICE THE PRODUCT of first and last term LAST TERM PERFECT SQUARE (positive)(positive)
  5. 5. PERFECT SQUARE TRINOMIAL 3. 𝑥2 + 5x + 6 ( )2 + 2( )( ) + ( )2 4. 9𝑥2 + 30xy + 25𝑦2 ( )2 + 2( )( ) + ( )2 5. 4𝑥2 + 2xy + 𝑦2 ( )2 + 2( )( ) + ( )2 x ?x ? 3x 5y3x 5y 2x 2x yy NOT NOT
  6. 6. FACTORING PERFECT SQUARE TRINOMIALS = ( 𝐱 + 𝒚) 𝟐(𝒙 𝟐 + 2xy + 𝒚 𝟐 ) FACTORED FORM = ( 𝐱 − 𝒚) 𝟐(𝒙 𝟐 - 2xy + 𝒚 𝟐 ) First FirstLast Last
  7. 7. FACTOR. 𝑥2 + 10x + 25 = ( 𝐱 + 𝒚) 𝟐 Check: ( )2 + 2( )( ) + ( )2 Factored Form: = ( + ) 𝟐 x 5x 5 x 5 16𝑥2 + 72x + 81 = ( 𝐱 + 𝒚) 𝟐 Check: ( )2 + 2( )( ) + ( )2 Factored Form: = ( + ) 𝟐 4x 94x 9 4x 9
  8. 8. FACTOR. 25𝑚2 − 20mn + 4𝑛2 = ( 𝐱 − 𝒚) 𝟐 Check: ( )2 − 2( )( )+( )2 Factored Form: = ( − ) 𝟐 5m 2n5m 2n 5m 2n 𝑥2 − 22x + 121 = ( 𝐱 − 𝒚) 𝟐 Check: ( )2 − 2( )( ) + ( )2 Factored Form: = ( − ) 𝟐 x 11x 11 x 11
  9. 9. FACTOR. 27𝑎2 + 72ab + 48𝑏2 Factor out 3: 3( + + ) Factored Form: 3( + ) 𝟐 16𝑏2 9𝑎2 24ab 3a 4b 4𝑥3 − 24𝑥2 + 36x Factor out 4x: 4x( - + ) Factored Form: 4x( − ) 𝟐 9𝑥2 6x x 3

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