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 \((x + 3)(x 鈥 4)(2x + 5)\)
- First, expand and simplify \( (x + 3)(x 鈥 4)\) to give \((x + 3)(x 鈥 4) = x^2 + 3x 鈥 4x - 12 = x^2 鈥 x 鈥 12\)
- Then, expand and simplify \((2x + 5)( x^2 鈥 x 鈥 12)\).
One way to organise this is using a grid:
Finally, collect like terms: \(2x^3 + 5x^2 鈥 2x^2 鈥 5x 鈥 24x 鈥 60 = 2x^3 + 3x^2 鈥 29x 鈥 60 \)
So \((x + 3)(x 鈥 4)(2x + 5) = 2x^3 + 3x^2 鈥 29x 鈥 60\)
Question
Expand and simplify \((x 鈥 2)(x + 6)(x 鈥 3)\)
First, expand and simplify \((x 鈥 2)(x + 6) \) to give \(x^2 鈥 2x + 6x -12 = x^2 +4x 鈥 12\).
Then, multiply this answer by \((x 鈥 3) \) to give \(x^3 + 4x^2 鈥 12x 鈥 3x^2 鈥 12x + 36\) which simplifies to give \(x^3 + x^2 鈥 24x + 36 \)
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