Cube of a Binomial
Expands the cube of a binomial expression.
Formula
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Example
(x+2)³ = x³ + 3x²(2) + 3x(4) + 8 = x³ + 6x² + 12x + 8.
How it works
When you cube a binomial, you are multiplying the same two-term expression by itself three times: (a+b)(a+b)(a+b). If you expand carefully, each term comes from choosing either a or b from each factor, which is why the coefficients become 1, 3, 3, 1. The pattern groups the products by how many times each variable appears, giving a^3, 3a^2b, 3ab^2, and b^3.
When to use it
Use this formula whenever you need to expand an expression like (x+4)^3 or simplify a cubic product in algebra. It is especially useful in factoring, polynomial multiplication, and checking answers in equation solving.
Worked example, step by step
(2y+3)^3 = (2y)^3 + 3(2y)^2(3) + 3(2y)(3^2) + 3^3 = 8y^3 + 3(4y^2)(3) + 3(2y)(9) + 27 = 8y^3 + 36y^2 + 54y + 27
Common mistakes to avoid
- Forgetting one of the middle terms and writing only four terms without the 3 coefficients
- Cubing each part separately as a^3 + b^3, which is not correct for a sum
- Not squaring or cubing the numeric coefficient correctly when a or b contains numbers
Did You Know?
Expanding (a+b)³ gives coefficients 1, 3, 3, 1 — the third row of Pascal's Triangle.
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