Expanding a Linear & a Quadratic (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Expanding a Linear & a Quadratic

How do I expand a linear expression and a quadratic expression?

• The same principles apply as to when you expand any combination of expressions or brackets

• Every term in the first bracket must be multiplied by every term in the second bracket

  • Expanding requires 6 multiplications in total

• When you multiply a quadratic by a linear term, as above, you will get a cubic

• As there are lots of terms to keep track of, you may prefer to use a grid

• To expand ,

  • Write out the brackets as row and column headings of a grid

  • They can be in either direction

  • Remember to write the appropriate sign in front of each term

• For each cell in the grid, multiply the term in the row heading by the term in the column heading

  • Remember that

• Add together all the terms inside the grid to get the answer

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• Collect like terms

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What if there are three brackets?

• You may have to expand three brackets like

• You know that the first two brackets expand to form a quadratic

  • Therefore will expand to form a cubic

• To expand three brackets,

  • Expand the first two brackets using your preferred method and simplify

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  • Multiply the result of this by the remaining bracket

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  • Simplify your answer

    •