Factorising quads diff 2 squares perfect squares
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The document focuses on factorizing quadratics using the difference of squares and perfect squares. It provides various examples and methodologies for expanding and factorizing quadratic expressions, illustrating the process with specific instances such as (x − 5)(x + 5) and 4x − 25. Additionally, it emphasizes the principles behind perfect square forms and their expansions.
Factorising quads diff 2 squares perfect squares
- 1. FACTORISING QUADRATICS Difference of 2 squares and Perfect Squares
- 2. DIFFERENCE OF 2 SQUARES • Investigate (expand): (x − 5)(x + 5) = (x + 2)(x − 2) = (3x − 6)(3x + 6) =
- 3. DIFFERENCE OF 2 SQUARES • Investigate (expand): (x − 5)(x + 5) = (x + 2)(x − 2) = (3x − 6)(3x + 6) =
- 4. DIFFERENCE OF 2 SQUARES • Investigate (expand): 2 2 (x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25 (x + 2)(x − 2) = (3x − 6)(3x + 6) =
- 5. DIFFERENCE OF 2 SQUARES • Investigate (expand): 2 2 (x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25 2 2 (x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4 (3x − 6)(3x + 6) =
- 6. DIFFERENCE OF 2 SQUARES • Investigate (expand): 2 2 (x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25 2 2 (x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4 2 (3x − 6)(3x + 6) = 9x + 18x − 18x − 36 2 = x − 36
- 7. DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b
- 8. FACTORISING USING DIFFERENCE OF 2 SQUARES • Factorise 2 x −36
- 9. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b • Factorise 2 x −36
- 10. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 x −36
- 11. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 x −36 a=x
- 12. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 x −36 a=x b=6
- 13. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 x −36 = (x + 6)(x − 6) a=x b=6
- 14. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 4x −25
- 15. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 4x −25 ( 2x ) −5 2 2
- 16. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 4x −25 ( 2x ) −5 2 2 a = 2x
- 17. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 4x −25 ( 2x ) −5 2 2 a = 2x b=5
- 18. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 4x −25 = (2x + 5)(2x − 5) ( 2x ) −5 2 2 a = 2x b=5
- 19. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 3x −15
- 20. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 3x −15 2 ( ) ( ) 2 3x − 15
- 21. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 3x −15 2 ( ) ( ) 2 3x − 15 a = 3x
- 22. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 3x −15 2 ( ) ( ) 2 3x − 15 a = 3x b = 15
- 23. FACTORISING USING DIFFERENCE OF 2 SQUARES 2 2 (a + b)(a − b) = a − b 2 2 a − b = (a + b)(a − b) • Factorise 2 3x −15 = ( 3x + 15 )( 3x − 15 ) 2 ( ) ( ) 2 3x − 15 a = 3x b = 15
- 24. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
- 25. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5)
- 26. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 27. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 28. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x b = −5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 29. PERFECT SQUARES • Investigate (expand): 2 (x − 5) = (x − 5)(x − 5) a=x b = −5 2ab = 2 × x × (−5) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 30. PERFECT SQUARES • Factorise 2 x − 8x + 16
- 31. PERFECT SQUARES • Factorise 2 x − 8x + 16 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 32. PERFECT SQUARES • Factorise 2 x − 8x + 16 a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 33. PERFECT SQUARES • Factorise 2 x − 8x + 16 a=x b = −4 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 34. PERFECT SQUARES • Factorise 2 x − 8x + 16 a=x b = −4 2ab = 2 × x × (−4) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 35. PERFECT SQUARES • Factorise 2 2 x − 8x + 16 = (x − 4) a=x b = −4 2ab = 2 × x × (−4) 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 36. PERFECT SQUARES • Factorise 2 x + 2 5x + 5
- 37. PERFECT SQUARES • Factorise 2 x + 2 5x + 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 38. PERFECT SQUARES • Factorise 2 x + 2 5x + 5 a=x 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 39. PERFECT SQUARES • Factorise 2 x + 2 5x + 5 a=x b= 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 40. PERFECT SQUARES • Factorise 2 x + 2 5x + 5 a=x b= 5 2ab = 2 × x × 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b
- 41. PERFECT SQUARES • Factorise 2 2 x + 2 5x + 5 = (x + 5 ) a=x b= 5 2ab = 2 × x × 5 2 2 2 (a + b) = a + 2ab + b 2 2 2 (a − b) = a − 2ab + b