Difference Of Cubes Formula
Difference Of Cubes Formula
The Difference Of Cubes Formula can be used to determine the cube differences between two numbers without having to compute the cubes themselves. One of the algebraic identities. The cube binomials are factorised using the formula for the difference of cubes. The a3-b3 formula is another name for the Difference Of Cubes Formula.
Students can check the difference of the cube formula, often known as the a3-b3 formula, by multiplying (a-b) by (a2 + ab + b2) and seeing if you obtain a3-b3.
The Difference Of Cubes Formula aids in determining a cube’s volume, diagonals, and surface area. The volume of a cube with an edge length equal to a particular number is directly represented by its cube. A cube is a solid three-dimensional object having six square faces and equal-length sides. One can find information about the Difference Of Cubes Formula on the Extramarks website or mobile application.
Formula for Difference of Cubes in Algebra
Equations with algebraic identities has the left side’s value equal to the right side’s value. Algebraic identities, as opposed to algebraic expressions, fulfil all possible values for the variables. The difference between cubes holds a central place in algebra, even though there are many algebraic identities.
When an integer or number is multiplied twice by itself, it becomes a cube (not a fraction). The difference (or change) of the cubes of two algebraic variables is what the formula’s name implies. For instance, a and b are two variables. Then, their cubes’ difference would be a3 – b3. The Difference Of Cubes Formula can be understood by referring to the study resources provided by Extramarks.
What Is the Difference Of Cubes Formula?
The Difference Of Cubes Formula, also known as the a3 – b3 formula, can be tested by multiplying (a – b) (a2 + ab + b2) and seeing if you get a3 – b3. The formula for the cubes’ difference is a3 – b3 = (a – b) (a2 + ab + b2).
The shorter diagonals on a cube’s square faces and the longer diagonals that go through its centre are of different lengths. One side’s length can be multiplied by the square root of three to find the major diagonal of a cube, which is the one that passes through the centre.
Examples Using Difference Of Cubes Formula
Example 1: Find the value of 1083 – 83 by using the Difference Of Cubes Formula.
Solution:
To find 1083 – 83.
Let us assume that a = 108 and b = 8.
We will substitute these in the Difference Of Cubes Formula.
a3 – b3 = (a – b) (a2 + ab + b2)
1083−83 = (108 − 8)(1082 + (108)(8) + 82) = (100)(11664 + 864 + 64) = (100)(12592) = 1259200
Answer: 1083 – 83 = 1,259,200.
Example 2: What is the value of 143 – 73?
Solution:
The difference between the Difference Of Cubes Formula is,
a3 – b3 = (a – b) (a2 + ab + b2)
From the given expression,
a = 14; b = 7
⇒ 143 – 73 = (14 – 7) (142 + (14)(7) + 72)
= 7 × (196 + 98 + 49)
= 7 × 343
= 2401
FAQs (Frequently Asked Questions)
1. What is the formula for factoring cubes?
The location of the minus sign distinguishes the two cube formulas: The minus sign acts in the linear factor, a – b, for cube difference, and in the quadratic factor, a2- ab + b2, for cube sum.
2. Which procedures are required to factor a sum of cubes?
Find the greatest common factor, or GCF, between the two terms to factor the sum of two cubes. Then, recast the original issue using those three parts as the difference between two perfect cubes.
3. How is the difference between two cubes factored?
The equation a^3 – b^3 = (a – b)(a^2 + ab + b^2) is to put this into practice, first cube root each of the ideal cubes. The second term is then subtracted from the first term to generate the first component. The squares of the first and second terms and their product are added to create the second factor.
