Cube Identities
Cube identities are standard formulas for expanding or factorising expressions involving cubes of binomials and sums or differences of cubes.
Practice This ConceptMain explanation
Teacher explanation
The key identities are (a+b)^3=a^3+3a^2b+3ab^2+b^3, (a-b)^3=a^3-3a^2b+3ab^2-b^3, a^3+b^3=(a+b)(a^2-ab+b^2), and a^3-b^3=(a-b)(a^2+ab+b^2). Signs must be watched carefully.
Example
x^3+8 = x^3+2^3 = (x+2)(x^2-2x+4).
Simple analogy
Cube signs follow the first bracket; sum gives minus in the middle factor.
Common confusion
Students often put all negative signs in (a-b)^3, but the third term +3ab^2 is positive.
Exam tip
In sum of cubes, the bracket sign is plus and the middle sign in the trinomial is minus; in difference of cubes, these signs reverse.
Answer writing and exam use
1-mark use
Write the exact meaning of cube identities in one clean line.
2-mark use
Define cube identities and add one example or condition.
3-mark use
Explain cube identities, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?