2.1- Introduction
Use and interpret algebraic manipulation, including:
• ab in place of a × b
• 3y in place of y + y + y and 3 × y
• a² in place of a × a, a³ in place of a × a × a, a² b in place of a × a × b
•  \(\frac{a}{b}\) in place of a ÷ b
• coefficients written as fractions rather than as decimals.
• brackets

2.2- Simplifying expressions
Simplify and manipulate algebraic expressions (including those involving surds) by:
● collecting like terms
● multiplying a single term over a bracket
● taking out common factors
● expanding products of two binomials
● factorising quadratic expressions of the form x² + bx + c, including the difference of two squares;
● simplifying expression

2.3- Indices
• Understand and use the rules of indices
– Simplify 2^-3 x 2⁴
3x^-4 x  \(\frac{2}{3} x^{\frac{1}{2}} \)
\(\frac{2}{5} x^{\frac{1}{2}} \)÷  \({2x^{-2}}\)

 \(\frac{(2x^5}{3})^3\)
• Use and interpret positive, negative, fractional and zero indices
e.g  \(5^{\frac{1}{2}}\)= \(\sqrt{5}\)
Evaluate 2⁵,4⁰,5², \(100^{frac{1}{2}\), \(8^{frac{-2}{3}\)
Solve 32^x= 2

2.4- Expanding and factorising 1
-Manipulate directed numbers
• use brackets and extract common factors
e.g factorise 9x²+ 15 y
• expand products of algebraic expressions
e.g expand 3x(2x-4y) ; (x+4)(x-7)
• Factorise where possible expressions of the form:
ax + bx + kay + kby
a² x²– b² y²
a²+ 2ab + b²
ax² + bx + c
• Manipulate algebraic fractions
e.g  \(\frac{x}{3} + \frac{x-4}{2}\); \(\frac{2x}{3} - \frac{3(x-5)}{2}\);\(\frac{3a}{4} × \frac{9a}{10}\);\(\frac{3a}{4} ÷ \frac{9a}{10}\);\(\frac{1}{x-2} + \frac{2}{x-3}\)
• Factorise and simplify rational expressions
e.g \(\frac{x^2 -2x}{x^2 - 5x+6}\)

2.5- Algebraic functions
-Substitute numerical values into formulae and expressions, including scientific formulae
-Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors
-Understand and use standard mathematical formulae; rearrange formulae to change the subject
-know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
-Where appropriate, interpret simple expressions as functions with inputs and outputs.

2.6-Summary and Review
BODMAS (/BIDMAS)
When simplifying an expression such as 3 + 4 × 5 – 4(3 + 2), remember to work it out in the following order: brackets, of (/indices), division, multiplication, addition, subtraction.
So do the thing in the brackets first, then any division, followed by multiplication and so on. The above is: 3 + 20 – 4 × 5 = 3 + 20 – 20 = 3 .
You mustn’t just work out the sum in the order that it is written down.

2.7- Assessment 2
Question 1 :
Calculate 9×5-2(7-4) ; (7-5)÷2+(93)×4 ?
Question 2 : Rearrange 2x =  \(\frac{y}{w}\)to make w the subject