1. Simplifying Squared & Cubed Expressions – Demonstration
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2. Express the area of this square algebraically.2𝑎 𝑎 𝑎
2𝑎 2
=4𝑎2 𝑎 𝑎2 𝑎2
2𝑎×2𝑎 2𝑎
2×𝑎×2×𝑎 𝑎 𝑎2 𝑎2
2×2×𝑎×𝑎
4×𝑎2

3. Express the areas of
these squares algebraically.
DEMO 3𝑏 3𝑏
3𝑏 2=9𝑏2
2𝑎 2=4𝑎2 5𝑏
Express the area of this cube algebraically. 2𝑑
1 2 𝑐
1 2 𝑐 2 = 1 4 𝑐2
5𝑏 2=25𝑏2
2𝑑 3=8𝑑3

4. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
Simplify:
2𝑏 2
Expand
& Simplify
2𝑏×2𝑏
2×𝑏× 2×𝑏
2×2×𝑏×𝑏
4×𝑏2
4𝑏2

5. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
Simplify:
3𝑐 2
Expand
& Simplify
3𝑐×3𝑐
3×𝑐×3×𝑐
3×3×𝑐×𝑐
9×𝑐2
9𝑐2

6. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
Simplify:
6𝑔 2
Expand
& Simplify
6𝑔×6𝑔
6×𝑔×6×𝑔
6×6×𝑔×𝑔
36×𝑔2
36𝑔2

7. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
6𝑔 2
5𝑘 2
Expand
& Simplify
Expand
& Simplify
6𝑔×6𝑔
5𝑘×5𝑘
6×𝑔×6×𝑔
5×𝑘×5×𝑘
6×6×𝑔×𝑔
5×5×𝑘×𝑘
36×𝑔2
25×𝑘2
36𝑔2
25𝑘2

8. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
6𝑔 2
4𝑚 2
Expand
& Simplify
Expand
& Simplify
6𝑔×6𝑔
4𝑚×4𝑚
6×𝑔×6×𝑔
4×𝑚×4×𝑚
6×6×𝑔×𝑔
4×4×𝑚×𝑚
36×𝑔2
16×𝑚2
36𝑔2
16𝑚2

9. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
Simplify:
2𝑎𝑏 2
Expand
& Simplify
2𝑎𝑏×2𝑎𝑏
2×𝑎×𝑏×2×𝑎×𝑏
2×2×𝑎×𝑎 ×𝑏×𝑏
4×𝑎2×𝑏2
4𝑎2𝑏2

10. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
2𝑎𝑏 2
3𝑑𝑒 2
Expand
& Simplify
Expand
& Simplify
2𝑎𝑏×2𝑎𝑏
3𝑑𝑒×3𝑑𝑒
2×𝑎×𝑏×2×𝑎×𝑏
3×𝑑×𝑒×3×𝑑×𝑒
2×2×𝑎×𝑎 ×𝑏×𝑏
3×3×𝑑×𝑑 ×𝑒×𝑒
4×𝑎2×𝑏2
9×𝑑2×𝑒2
4𝑎2𝑏2
9𝑑2𝑒2

11. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
Simplify:
3𝑎2𝑏 2
Expand
& Simplify
3𝑎2𝑏×3𝑎2𝑏
3×𝑎×𝑎×𝑏×3×𝑎×𝑎×𝑏
3×3×𝑎×𝑎 ×𝑎 ×𝑎×𝑏×𝑏
9×𝑎4×𝑏2
9𝑎4𝑏2

12. Simplifying Squared & Cubed Expressions
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
3𝑎2𝑏 2
5𝑓ℎ2 2
Expand
& Simplify
Expand
& Simplify
3𝑎2𝑏×3𝑎2𝑏
5𝑓ℎ2×5𝑓ℎ2
3×𝑎×𝑎×𝑏×3×𝑎×𝑎×𝑏
5×𝑓×ℎ×ℎ×5×𝑓×ℎ×ℎ
3×3×𝑎×𝑎 ×𝑎 ×𝑎×𝑏×𝑏
5×5×𝑓×𝑓 ×ℎ ×ℎ×ℎ×ℎ
9×𝑎4×𝑏2
25×𝑓2×ℎ4
9𝑎4𝑏2
25𝑓2ℎ4

13. 2𝑐2𝑑 3 2𝑐2𝑑×2𝑐2𝑑 ×2𝑐2𝑑 8×𝑐6×𝑑3 8𝑐6𝑑3 2×𝑐×𝑐×𝑑×2×𝑐×𝑐×𝑑 ×2×𝑐×𝑐×𝑑
DEMO
Simplifying Squared & Cubed Expressions
Arghhh…!!!
There must be an easier way!
Simplify:
2𝑐2𝑑 3
Expand
& Simplify
2𝑐2𝑑×2𝑐2𝑑 ×2𝑐2𝑑
2×𝑐×𝑐×𝑑×2×𝑐×𝑐×𝑑 ×2×𝑐×𝑐×𝑑
2×2×2×𝑐×𝑐 ×𝑐 ×𝑐×𝑐×𝑐 ×𝑑×𝑑×𝑑
8×𝑐6×𝑑3
8𝑐6𝑑3

14. DEMO
Simplifying Squared & Cubed Expressions
Simplify:
3𝑎𝑏 2
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
(3)2=9
𝑎 2=𝑎2
𝑏 2=𝑏2
9𝑎2𝑏2

15. DEMO
Simplifying Squared & Cubed Expressions
Simplify:
4𝑎2𝑏 2
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
(4)2=16
(𝑎2)2=𝑎4
𝑏 2=𝑏2
16𝑎4𝑏2

16. DEMO
Simplifying Squared & Cubed Expressions
Simplify:
3𝑎3𝑏2 3
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
3 3=27
𝑎3 3=𝑎9
𝑏2 3=𝑏6
27𝑎9𝑏6

17. 3𝑎3𝑏2 3 2𝑎𝑏2 2 27𝑎9𝑏6 4𝑎2𝑏4 3 3=27 22=4 𝑎3 3=𝑎9 𝑎 2=𝑎2 𝑏2 3=𝑏6 𝑏2 2=𝑏4
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
3𝑎3𝑏2 3
2𝑎𝑏2 2
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
3 3=27
22=4
𝑎3 3=𝑎9
𝑎 2=𝑎2
𝑏2 3=𝑏6
𝑏2 2=𝑏4
27𝑎9𝑏6
4𝑎2𝑏4

18. DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
3𝑎3𝑏2 3
5𝑎3𝑏2 2
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
3 3=27
52=25
𝑎3 3=𝑎9
𝑎3 2=𝑎6
𝑏2 3=𝑏6
𝑏2 2=𝑏4
27𝑎9𝑏6
25𝑎6𝑏4

19. DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify:
3𝑎3𝑏2 3
5𝑎3𝑏4 3
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
3 3=27
53=125
𝑎3 3=𝑎9
𝑎3 3=𝑎9
𝑏2 3=𝑏6
𝑏4 3=𝑏12
27𝑎9𝑏6
125𝑎9𝑏12

20. 4𝑎2𝑏 2 16𝑎4𝑏2 2𝑎 2= 3𝑐𝑑 2= 3𝑒 3=27 𝑓2𝑔 2= 2𝑒ℎ2 2= 5𝑘3𝑔2 3= 4𝑡4𝑠2𝑝 3=
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify these expressions:
2𝑎 2=
3𝑐𝑑 2=
4𝑎2𝑏 2
3𝑒 3=27
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
𝑓2𝑔 2=
2𝑒ℎ2 2=
(4)2=16
5𝑘3𝑔2 3=
(𝑎2)2=𝑎4
4𝑡4𝑠2𝑝 3=
(𝑏)2=𝑏2
1 2 𝑚3𝑛2 3 =
16𝑎4𝑏2

21. 4𝑎2𝑏 2 16𝑎4𝑏2 2𝑎 2=4𝑎2 3𝑐𝑑 2=9𝑐2𝑑2 3𝑒 3=27𝑒3 𝑓2𝑔 2=𝑓4𝑔2 2𝑒ℎ2 2=4𝑒2ℎ4
DEMO
Simplifying Squared & Cubed Expressions
YOUR TURN
Simplify:
Simplify these expressions:
2𝑎 2=4𝑎2
3𝑐𝑑 2=9𝑐2𝑑2
4𝑎2𝑏 2
3𝑒 3=27𝑒3
Square/Cube each term within the brackets.
Remember!
Indices squared or cubed are multiplied.
𝑓2𝑔 2=𝑓4𝑔2
2𝑒ℎ2 2=4𝑒2ℎ4
(4)2=16
5𝑘3𝑔2 3=125𝑘9𝑔6
(𝑎2)2=𝑎4
4𝑡4𝑠2𝑝 3=64𝑡12𝑠6𝑝3
(𝑏)2=𝑏2
1 2 𝑚3𝑛2 3 = 1 8 𝑚9𝑛6
16𝑎4𝑏2

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