Expanding triple brackets

When we have more than two sets of brackets, we can expand them separately - first expand two of the brackets, then expand the result with the remaining bracket.

Example: Expand (2x + 3)(x + 4)(x - 3) using the grid method

First, expand the first two brackets, (2x + 3)(x + 4):

\timesx4
2x
3
\timesx4
2x2x^28x
33x12

This simplifies to 2x^2 + 11x + 12.

Now, expand this result with the remaining bracket, (x - 3):

\times2x^211x12
x
-3
\times2x^211x12
x2x^311x^212x
-3-6x^2-33x-36

This simplifies to 2x^3 + 5x^2 - 21x - 36.

Answer: 2x^3 + 5x^2 - 21x - 36

flashcards

QuestionAnswer
How do you expand three sets of brackets?First expand two of the brackets, then expand the result with the remaining bracket.
In the example (2x + 3)(x + 4)(x - 3), what is the result of expanding the first two brackets (2x + 3)(x + 4)?2x^2 + 11x + 12
In the example, after expanding (2x + 3)(x + 4) to 2x^2 + 11x + 12, what is the next step?Expand (2x^2 + 11x + 12) with the remaining bracket (x - 3).
What is the final expanded form of (2x + 3)(x + 4)(x - 3)?2x^3 + 5x^2 - 21x - 36
In the example, what are the three terms obtained when multiplying x by 2x^2, 11x, and 12?2x^3, 11x^2, and 12x
In the example, what are the three terms obtained when multiplying -3 by 2x^2, 11x, and 12?-6x^2, -33x, and -36