# 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 $$x^3 + x^2 – 24x + 36$$.