Algebraic Manipulation

The toolkit for rearranging and simplifying algebraic expressions - expanding brackets, factorising, and handling algebraic fractions, all skills you'll reuse constantly in later topics.

  • Expanding brackets
  • Factorising
  • Algebraic fractions

Lessons for Algebraic Manipulation

Expanding Brackets

Removing bracketsThink of expanding brackets like handing out sweets: everything outside the bracket must be given to everything inside, one …

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Factorising

Factorising is the reverse of expandingLike packing sweets back into a labelled bag - you're looking for what's common.Common factor6x …

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Algebraic Fractions

SimplifyingCancel common factors, exactly like simplifying 6/8 to 3/4 - just with letters mixed in.Example: (x²-9)/(x+3) = (x-3)(x+3)/(x+3) = x-3Adding …

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Exercises for Algebraic Manipulation

Expand and simplify

Expand 4(2x - 3)Expand -2(x + 5)Expand and simplify (x+3)(x+2)Expand and simplify (x-4)(x+4)Expand and simplify (3x-1)(2x+5)

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Factorise fully

Factorise 8x + 12Factorise x² + 9x + 20Factorise x² - 5x + 6Factorise x² - 49Factorise 2x² + 7x …

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Simplify algebraic fractions

Simplify (x²-4)/(x+2)Simplify (3x²+6x)/(3x)Write as a single fraction: 2/x + 3/(x+2)Write as a single fraction: 5/(x-1) - 2/(x+1)

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