Examples on Sum of Cubes Formula
Example 1: Factorize 343a3 + 216 using sum of cubes.
Solution:
Given,
343a3 + 216 = (7a)3 + (6)3
Since, a3 + b3 = (a + b)(a2 β ab + b2)
β 343a3 + 216 = (7a + 6)[(7a)2 β (7a)(6) + (6)2]
β 343a3 + 216 = (7a + 6)[49a2 β 42a + 36]
Example 2: Factorize 8p3 + 27 using sum of cubes.
Solution:
Given,
8p3 + 27 = (2p)3 + (3)3
Since, a3 + b3 = (a + b)(a2 β ab + b2)
β 8p3 + 27 = (2p + 3)[(2p)2 β (2p)(3) + (3)2]
β 8p3 + 27 = (2p + 3)[4p2 β 6p + 9]
Example 3: Factorize 27t3 + 125 using the sum of cubes.
Solution:
Given,
27t3 + 125 = (3t)3 + (5)3
Since, a3 + b3 = (a + b)(a2 β ab + b2)
β 27t3 + 125 = (3t + 5)[(3t)2 β (3t)(5) + (5)2]
β 27t3 + 125 = (3t + 5)[9t2 β 15t + 25]
Example 4: Factorize 64s3 + 125 using sum of cubes.
Solution:
Given,
64s3 + 125 = (4s)3 + (5)3
Since, a3 + b3 = (a + b)(a2 β ab + b2)
β 64s3 + 125 = (4s + 5)[(8s)2 β (4s)(5) + (5)2]
β 64s3 + 125 = (8s + 5)[64s2 β 20s + 25]
Example 5: Factorize 512 + 729v3 using the sum of cubes formula.
Solution:
512 + 729v3 = (8)3 + (9v)3
Since, a3 + b3 = (a + b)(a2 β ab + b2)
β 512 + 729v3 = (8 + 9v)[(8)2 β (8)(9v) + (9v)2]
β 512 + 729v3 = (8 + 9v)[64 β 72v + 729v2]
a3 + b3 Formula
a3 + b3 formula which is also called the sum of cubes formula, in algebra is the fundamental algebra formula that is used to find the sum of cubes of any two numbers without actually calculating their cubes. a3 + b3 formula is also used to find the factors of a3 + b3. This helps to simplify various algebraic expressions.
In this article, we will learn about, the a3 + b3 formula, factors of a3 + b3, examples, and others in detail.
Table of Content
- What is a3 + b3 Formula?
- What is Sum of Cubes Formula?
- a3 + b3 Formula Proof
- Examples on Sum of Cubes Formula
- a3 + b3 Formula β FAQs