1. Expanding, Factors,simplifying
Algebra
Expanding, Factors,simplifying

2. Do now 𝑎−𝑏−𝑐 2 −𝑥 4𝑥−1 2 −𝑥(2+3𝑥) 𝑥 2 +3𝑥+2 3𝑥 2 −𝑥−2
Expand and Simplify
𝑎−𝑏−𝑐 2
−𝑥 4𝑥−1 2 −𝑥(2+3𝑥)
Factorise
𝑥 2 +3𝑥+2
3𝑥 2 −𝑥−2

3. Factorising polynomials
8𝑥 2 +6𝑥−35
𝑤𝑥+𝑢𝑥+𝑤𝑦+𝑢𝑦

4. Rational expressions
(3 𝑥 2 𝑦) 3 ×4 (𝑥𝑦) 𝑥 5 𝑦 7
𝑝 𝑥 2 + 𝑞 𝑥𝑦

5. 𝑥 2 −𝑥−12 𝑥 2 −16
𝑥 2 +𝑥−6 𝑥 2 −𝑥 × 𝑥 2 −1 2𝑥−4

6. Practice ESA page 143 onwards Theta page 20 onwards
Theta page 9 onwards (Language practice)

7. Do now 𝑥 2 −8𝑥+7 𝑥−1 𝑖𝑓 𝑥=2, 𝑥−2 𝑥+2 = 𝑓 𝑥 = 𝑥 2 +3𝑥−1, 𝑓𝑖𝑛𝑑 𝑓(−1)
State the operation you would use and give the end result (Expand, Factorise, Solve, Evaluate, Simplify)
𝑥 2 −8𝑥+7 𝑥−1
(𝑥−3) 2 =16
𝑖𝑓 𝑥=2, 𝑥−2 𝑥+2 = 𝑓 𝑥 = 𝑥 2 +3𝑥−1, 𝑓𝑖𝑛𝑑 𝑓(−1)

8. Do now
The roots of an equation are 𝑥 1 = 3 2 𝑎𝑛𝑑 𝑥 2 =− show this equation in terms of 𝑎 𝑥 2 +𝑏𝑥+𝑐=0.
𝑥 2 +8𝑥+100= 𝑥 2 +8𝑥+64+___________=0
so 𝑥 2 +8𝑥+100=(𝑥+4)+________

9. Write with a positive index:
Negative power means take the reciprocal.
Negative power means take the reciprocal.
Simplify.

10. Negative power means take the reciprocal.
8.02B
Evaluate:
Negative power means take the reciprocal.
Work out the power.

11. Negative power means take the reciprocal.
8.02B
Evaluate:
Negative power means take the reciprocal.
Work out the power.
Work out.
Alternatively:
Write 0.5 as a fraction.
Negative power means take the reciprocal.
Work out.

12. Negative power means take the reciprocal.
Write
as a fraction.
Negative power means take the reciprocal.
The reciprocal of 2 3 is
Work out the power.

13. Answer using positive indices only
8.03
Simplify
(a)
(b)
Answer using positive indices only
(a)
Multiply the numbers.

14. The denominator of 5 means a 5th root.

15. The denominator of 3 means a 3rd root.
8.04B
The denominator of 3 means a 3rd root.
Evaluate.

16. The 4th root means there is a 4 in the denominator of the power.
8.04C
The 4th root means there is a 4 in the denominator of the power.

17. Raise each term to the power of .
8.04D
Raise each term to the power of . 1 2
As a power of means a square root, take the square root of 64. 1 2

18. Multiply for the power of x.
8.04D
Multiply for the power of x.

19. Evaluate the fractional power (a square root).
Break up the fractional power into two powers to get a simple root raised to a simple power.
Evaluate the fractional power (a square root).
Evaluate the power 3.

20. Write the square root as power .
8.04F
Write the square root as power . 1 2
A power of a power means multiply the powers.

21. The negative sign in the power means a reciprocal.
The 3 in the denominator of the power means a cube root.

22. Negative power. Write term in the denominator of a fraction.
8.05B
Evaluate
(a)
(b)
(a)
Negative power. Write term in the denominator of a fraction.
Write the term in the denominator as a root.
Evaluate the root.

23. Negative power. Take reciprocal of fraction.
8.05B
Evaluate
(a)
(b)
(b)
Negative power. Take reciprocal of fraction.
Write the term in the denominator of the power as a root.
Evaluate the root.
Evaluate the power.

24. Note that 4 = 22. Therefore replace 4 by its equivalent 22.
8.06
Simplify
Note that 4 = 22. Therefore replace 4 by its equivalent 22.
Multiply out the power of a power.
Subtract powers to divide.

25. Practice
Theta pages 16 and 76