Topic Details (Notes format)

How to Factor the Sum or Difference of Cubes

Subject: Mathematics

Book: Maths Mastery

Sum of cubes a³ + b³ factors into (a + b)(a² – ab + b²), while difference of cubes a³ – b³ factors into (a – b)(a² + ab + b²). For instance, x³ – 8 = (x – 2)(x² + 2x + 4). These patterns appear frequently in polynomial algebra and advanced factorization tasks. You’ll see them in integral calculus (factoring integrands), economic models (cubic cost functions), and more. Knowing how to handle sums/differences of cubes fosters swift resolution of higher-order polynomial problems.

Practice Questions

If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

View Question

If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

View Question

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

View Question

What is the area of a sector of a circle with radius 14 cm and central angle 90°?

View Question

The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

View Question

If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

View Question

If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

View Question

What is the greatest common divisor (GCD) of 36 and 48?

View Question

If a = 4 and b = 5, what is the value of (a+b)^2?

View Question

If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

View Question