factoring perfect square trinomials.pdf
- 1. Grade 8 – Mathematics Quarter I FACTORING PERFECT SQUARE TRINOMIALS
- 2. Objectives: 1. identify whether or not an expression is a perfect square trinomial; and 2. factor perfect square trinomials completely.
- 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. PERFECT SQUARE TRINOMIAL 1. 𝑥2 + 2xy + 𝑦2 ( )2 + 2( )( ) + ( )2 2. 4𝑥2 + 20x + 25 ( )2 + 2( )( ) + ( )2 x y x y 2x 5 2x 5 FIRST TERM PERFECT SQUARE MIDDLE TERM TWICE THE PRODUCT of first and last term LAST TERM PERFECT SQUARE (positive) (positive)
- 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 5y 3x 5y 2x 2x y y NOT NOT
- 6. FACTORING PERFECT SQUARE TRINOMIALS = (𝐱 + 𝒚)𝟐 (𝒙𝟐 + 2xy + 𝒚𝟐 ) FACTORED FORM = (𝐱 − 𝒚)𝟐 (𝒙𝟐 - 2xy + 𝒚𝟐 ) First First Last Last
- 7. FACTOR. 𝑥2 + 10x + 25 = (𝐱 + 𝒚)𝟐 Check: ( )2 + 2( )( ) + ( )2 Factored Form: = ( + )𝟐 x 5 x 5 x 5 16𝑥2 + 72x + 81 = (𝐱 + 𝒚)𝟐 Check: ( )2 + 2( )( ) + ( )2 Factored Form: = ( + )𝟐 4x 9 4x 9 4x 9
- 8. FACTOR. 25𝑚2 − 20mn + 4𝑛2 = (𝐱 − 𝒚)𝟐 Check: ( )2 − 2( )( )+( )2 Factored Form: = ( − )𝟐 5m 2n 5m 2n 5m 2n 𝑥2 − 22x + 121 = (𝐱 − 𝒚)𝟐 Check: ( )2 − 2( )( ) + ( )2 Factored Form: = ( − )𝟐 x 11 x 11 x 11
- 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 9 𝑥2 6x x 3