Cube formulas in algebra

In this topic cube formulas in algebra we are going to discuss about two formulas which are being used to expand the terms like in the form (a - b)³. We are going to see some of the example problem.

After getting clear of using this you can try the worksheet also.We have given this worksheet for the purpose of making practice.If you practice this worksheets it will become easy to solve problems in the topic algebra.We will use these formulas in most of the problem. Question 1 :

Expand (x - 1) ³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "x"and instead of 'b' we have "1" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b

(x - 1)³  = (x)³ - 3 (x)²(1)+ 3 (x)(1)² - (1)³

= x³- 3 (x²)(1) + 3(x)(1) - 1

= x³ - 3 x ² + 3 x - 1

We will see another example in cube formulas in algebra.

Question 2:

Expand (2a²-3)³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "2a²"and instead of 'b' we have "3" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b

(2a²- 3)³  = (2a²)³ - 3 (2a²)²(3)+ 3 (2a²)(3)² - (3)³

= 8a⁶- 3(4)(3) a⁴ + 3(2)(9)a² - 27

= 8a⁶- 36 a⁴ + 54a² - 27

Question 3:

(2b-3d)³

Solution:

Here the question is in the form of (a-b)³.  Instead of 'a' we have "2b"and instead of 'b' we have "3d" . Now we need to apply the formula a³- 3a² b + 3ab² - b³ and we need to apply those values instead of a and b

(2b- 3d)³  = (2b)³ - 3 (2b)²(3d)+ 3 (2b)(3d)² - (3d)³

= 8b³ - 3(4)3b²d +3(2)(9)bd² - 27d³

= 8b³ - 36b²d +54 bd² - 27 d³

Students can go through these examples given in this page'Cube formulas in algebra' and become expert in cube formulas. They can try  to solve some more problems given below on their own. If you have any doubt you can contact us through mail, we will help you to clear your doubts.

Problems for practice:

1. (a-3)³

2. (2x-4)³

3. (b-2)³ 