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Algebraic Manipulation

infoWhy this? Algebraic manipulation enables us to express general relationships concisely and transform expressions without changing their value. Collecting terms, applying index laws, expanding brackets, and substituting values develop fluency with structure and equivalence.

scheduleWhy now? This unit builds on arithmetic operations, powers, and number structure as we move from calculating with particular numbers to reasoning with general quantities. Secure notation and manipulation are needed before solving equations, generating sequences, and graphing relationships.

neurologyYou need to know

  • Like terms are terms in an algebraic expression that have exactly the same variable parts, raised to the same powers.
  • Terms can only be collected (added or subtracted) if they are like terms.
  • For positive integers `m` and `n`, the index laws used in this unit are `a^m \times a^n = a^{m+n}`, `\frac{a^m}{a^n} = a^{m-n}` when `a \neq 0` and `m \geq n`, and `(a^m)^n = a^{m \times n}`; additionally, `a^0 = 1` when `a \neq 0`, so this does not include `0^0`.
  • The laws of indices apply to both numerical and algebraic bases.
  • When multiplying or dividing algebraic terms, coefficients are multiplied or divided, and the index laws are applied to the variables.
  • Expanding a single bracket involves multiplying each term inside the bracket by the term outside the bracket.
  • Substitution means replacing variables in an expression with given numerical values, which may be positive or negative.
  • The order of operations (BIDMAS) must be followed when simplifying expressions and substituting values.

rocket_launchYou must be able to

  • Identify and collect like terms in an algebraic expression to simplify it Exemplification.
  • Apply the laws of indices for same-base multiplication, same-base division, and powers of powers to write numerical and algebraic expressions as a single power without using negative or fractional indices Exemplification.
  • Multiply and divide algebraic terms, simplifying the result using index laws without using negative or fractional indices Exemplification.
  • Expand expressions involving a single bracket, such as `a(b + c)` Exemplification.
  • Substitute positive and negative values into basic linear expressions and evaluate the result correctly Exemplification Exemplification.


Revision Quiz

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