Expanding three brackets - Higher
To expand three brackets, expand and simplify two of the brackets then multiply the resulting expression by the third bracket.
Example
- expand and simplify \((x + 3)(x - 4)(2x + 5)\)
- first, expand and simplify \( (x + 3)(x - 4)\) to give \((x + 3)(x - 4) = x^2 + 3x - 4x - 12 = x^2 - x - 12\)
- then, expand and simplify \((2x + 5)( x^2 - x - 12)\)
One way to organise this is using a grid:
Finally, collect like terms: \(2x^3 + 5x^2 - 2x^2 - 5x - 24x - 60 = 2x^3 + 3x^2 - 29x - 60 \)
So, \((x + 3)(x - 4)(2x + 5) = 2x^3 + 3x^2 - 29x - 60\)
Question
Expand and simplify \((x - 2)(x + 6)(x - 3)\)
First, expand and simplify \((x - 2)(x + 6) \) to give \(x^2 - 2x + 6x - 12 = x^2 +4x - 12\).
Then, multiply this answer by \((x - 3) \) to give \(x^3 + 4x^2 - 12x - 3x^2 - 12x + 36\) which simplifies to give \(x^3 + x^2 - 24x + 36 \).
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