Expanding Three Brackets: Explanation, Examples and Questions
Expanding three brackets is an algebraic skill that might seem difficult at first but is actually quite a simple skill. It can be required for use in solving quadratic equations and sketching quadratic graphs.
What Does ‘Expanding Triple Brackets’ Mean?
Expanding triple brackets means to multiply three brackets together so that the product of three expressions can be written as one single expression.
For example, (x - 3)(x + 2)(x + 5) means (x - 3) multiplied by (x + 2) and then multiplied again by (x + 5).
This process is the opposite of factorising cubics and can be useful in solving various types of algebraic problems.
Here are some examples of expanding triple brackets:
\((x + 1)(x + 2)(x + 3) = x^3 + 6x^2 + 11x + 6\)
\((y + 2)(y - 3)(y + 4) = y^3 + 3y^2 - 10y - 24\)
\((2x + 1)(x - 4)(x + 5) = 2x^3 + 3x^2 - 39x - 20\)
In each case, the brackets on the left side of the equation have been expanded (multiplied) and rewritten without brackets on the right side of the equation.
If you’re not sure how this was done, don’t worry! We have plenty of examples.