Topic Details (Notes format)

What is the formula for a^3 + b^3?

Subject: Mathematics

Book: Algebraic Identities

The sum of cubes of two variables (a^3 + b^3) can be factorized using the following algebraic identity:

(a^3 + b^3) = (a + b)(a^2 - ab + b^2)

### Key Points:
1. **Expansion**: When expanded, (a + b)(a^2 - ab + b^2) reconverts to a^3 + b^3.
2. **Complementary Formula**: The difference of cubes identity is:

(a^3 - b^3) = (a - b)(a^2 + ab + b^2)

3. **Usage**: These sum and difference of cubes formulas are essential for factorizing polynomials, simplifying algebraic expressions, and solving higher-level algebra problems.

Remembering this simple formula helps in quickly dealing with cubic expressions in algebraic contexts.

Practice Questions

What is the sum of all odd numbers from 1 to 99?

View Question

The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

View Question

A man spends 75% of his income and saves Rs. 600. What is his total income?

View Question

If x^2 + 4x + 4 = 0, what is the value of x?

View Question

If 2x - 3 = 7, what is the value of x?

View Question

If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

View Question

The base of a triangle is 10 cm and its height is 6 cm. What is its area?

View Question

If 2x = 16, what is the value of x?

View Question

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

If sin(A) = 1/2 and A is acute, what is the value of A?

View Question