Factorising quads diff 2 squares perfect squares

Lesson that gives examples of how to factorise quadratic equations using the difference of 2 squares rule and the properties of 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):
(x−5)(x+5)=
(x+2)(x−2)=(3x−6)(3x+6)=
x
2
−5x+5x−25=x
2
−25

5. DIFFERENCE OF 2 SQUARES
•Investigate (expand):
(x−5)(x+5)=
(x+2)(x−2)=(3x−6)(3x+6)=
x
2
−5x+5x−25=x
2
−25x
2
+2x−2x−4=x
2
−4

6. DIFFERENCE OF 2 SQUARES
•Investigate (expand):
(x−5)(x+5)=
(x+2)(x−2)=(3x−6)(3x+6)=
x
2
−5x+5x−25=x
2
−25x
2
+2x−2x−4=x
2
−49x
2
+18x−18x−36
=x
2
−36

7. DIFFERENCE OF 2 SQUARES
(a+b)(a−b)=a
2
−b
2

8. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
x
2
−36

9. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
2x
2
−36

10. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
2x
2
−36a
2
−b
2
=(a+b)(a−b)

11. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
2x
2
−36
a=x
a
2
−b
2
=(a+b)(a−b)

12. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
2x
2
−36
b=6
a=x
a
2
−b
2
=(a+b)(a−b)

13. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
2x
2
−36
b=6
a=x
=(x+6)(x−6)
a
2
−b
2
=(a+b)(a−b)

14. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
24x
2
−25a
2
−b
2
=(a+b)(a−b)

15. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
24x
2
−25a
2
−b
2
=(a+b)(a−b)
2x()
2
−5
2

16. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
24x
2
−25
a=2x
a
2
−b
2
=(a+b)(a−b)
2x()
2
−5
2

17. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
24x
2
−25
b=5a=2x
a
2
−b
2
=(a+b)(a−b)
2x()
2
−5
2

18. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
24x
2
−25
b=5a=2x
=(2x+5)(2x−5)
a
2
−b
2
=(a+b)(a−b)
2x()
2
−5
2

19. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
23x
2
−15a
2
−b
2
=(a+b)(a−b)

20. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
23x
2
−15a
2
−b
2
=(a+b)(a−b)3x
()2
−15
()
2

21. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
23x
2
−15
a=3x
a
2
−b
2
=(a+b)(a−b)3x
()2
−15
()
2

22. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
23x
2
−15
b=15a=3x
a
2
−b
2
=(a+b)(a−b)3x
()2
−15
()
2

23. FACTORISING USING
DIFFERENCE OF 2 SQUARES
•Factorise
(a+b)(a−b)=a
2
−b
23x
2
−15
b=15a=3x
=(3x+15)(3x−15)a
2
−b
2
=(a+b)(a−b)3x
()2
−15
()
2

24. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)

25. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)

26. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2

27. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
a=x

28. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=−5
a=x

29. PERFECT SQUARES
•Investigate (expand):
(x−5)
2
=(x−5)(x−5)
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=−5
a=x2ab=2×x×(−5)

30. PERFECT SQUARES
•Factorise
x
2
−8x+16

31. PERFECT SQUARES
•Factorise
x
2
−8x+16
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2

32. PERFECT SQUARES
•Factorise
x
2
−8x+16
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
a=x

33. PERFECT SQUARES
•Factorise
x
2
−8x+16
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=−4a=x

34. PERFECT SQUARES
•Factorise
x
2
−8x+16
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=−4a=x2ab=2×x×(−4)

35. PERFECT SQUARES
•Factorise
x
2
−8x+16
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=−4a=x2ab=2×x×(−4)
=(x−4)
2

36. PERFECT SQUARES
•Factorise
x
2
+25x+5

37. PERFECT SQUARES
•Factorise
x
2
+25x+5
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2

38. PERFECT SQUARES
•Factorise
x
2
+25x+5
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
a=x

39. PERFECT SQUARES
•Factorise
x
2
+25x+5
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=5
a=x

40. PERFECT SQUARES
•Factorise
x
2
+25x+5
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=5
a=x
2ab=2×x×5

41. PERFECT SQUARES
•Factorise
x
2
+25x+5
(a+b)
2
=a
2
+2ab+b
2
(a−b)
2
=a
2
−2ab+b
2
b=5
a=x
2ab=2×x×5
=(x+5)
2