Algebraic Manipulation

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infoWhy this? More advanced algebraic manipulation enables us to form, simplify, expand, and factorise expressions while preserving equivalence. Understanding expansion and factorisation as inverse processes reveals structure and supports efficient problem-solving.

scheduleWhy now? Year 7 established like terms, index laws, substitution, and single-bracket expansion. We now combine these skills in longer expressions and introduce factorisation before solving more complex equations and working with quadratics.

Like terms in algebra are terms that have exactly the same variable parts, including the same powers.
Collecting like terms means combining terms with the same variable parts by adding or subtracting their coefficients.
For positive `a`, integers `m` and `n`, and a positive integer `r`, the laws of indices used in this unit are `a^m \times a^n = a^{m+n}`, `\frac{a^m}{a^n} = a^{m-n}`, `a^0 = 1`, `(a^m)^n = a^{mn}`, `a^{-m} = \frac{1}{a^m}`, and `a^{\frac{1}{r}} = \sqrt[r]{a}`.
Expanding a single bracket means multiplying each term inside the bracket by the term outside the bracket.
Substitution in algebra means replacing variables with given numerical values.
An algebraic expression is a combination of numbers, variables, and operations such as addition, subtraction, multiplication, and division.
Factorising an expression means writing it as a product of its factors, usually by taking out the highest common factor and writing the expression in bracketed form.

rocket_launchYou must be able to

Form algebraic expressions from worded descriptions or real-life contexts.
Simplify more complex algebraic expressions by multiplying or dividing terms, including those with more than one variable or power.
Expand and simplify expressions involving multiple single brackets, such as `(a + b) + (c + d)` or `a(b + c) + d(e + f)`.
Factorise algebraic expressions into a single bracket by taking out the highest common factor.

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