To expand three brackets, expand two brackets first and simplify the result.
Then multiply that expression by the third bracket, making sure every term is multiplied before collecting like terms.
Common mistake: Do not try to multiply only the first terms and the number terms. For \((x + 2)(x + 3)(x + 4)\), expand two full brackets first, then multiply the whole result by the third bracket.
Worked example:
Expand and simplify \((x + 2)(x + 3)(x - 1)\).
Step 1
Expand two brackets first.
\[(x + 2)(x + 3) = x^2 + 5x + 6\]
Step 2
Multiply this result by the third bracket and collect like terms.
\[(x^2 + 5x + 6)(x - 1) = x^3 + 4x^2 + x - 6\]
Answer:
\[(x + 2)(x + 3)(x - 1) = x^3 + 4x^2 + x - 6\]
Worked example:
Expand and simplify \((2x - 1)(x + 4)(x - 3)\).
Step 1
Expand the two simpler brackets first.
\[(x + 4)(x - 3) = x^2 + x - 12\]
Step 2
Multiply by the remaining bracket and collect like terms.
\[(2x - 1)(x^2 + x - 12) = 2x^3 + x^2 - 25x + 12\]
Answer:
\[(2x - 1)(x + 4)(x - 3) = 2x^3 + x^2 - 25x + 12\]