a+b whole cube | A Plus B Whole Cube Formula

Assume that a and b are two variables that, in algebraic form, stand in for two terms. In mathematics, the sum of the two terms is denoted by the symbol(a+b). It is both a binomial and an algebraic expression. In mathematics, the cube of the sum of the terms a and b, or a binomial, is represented by the following notation:(a+b)3

Introduction of a+b whole cube

When a cube is added with b cube and then the result is added with three times a multiply by b, and addition of a and b, then the a plus b whole cube is obtained.

This can be represented as-

(a + b)3 =a³ + b3 + 3ab(a+b)

The formula for a plus b whole cube can also be written as a cube plus b cube plus three a square b plus three a, b square. It is written below-

(a + b)3 = a3+ b3 + 3a2b+3ab2

In mathematics, the plus b whole cubed algebraic identity is called in the following three ways-

• The cube of the sum of two terms rules.

• The cube of a binomial identity.

• The special binomial product formula.

Usage

In the following two instances, the cube of the sum of two terms rule is applied as a formula.

1. Expansion

The total of the cubes of the two terms and their product, multiplied by three, form the cube of the sum of the two terms.

(a + b)3 = a3+ b3 + 3ab(a+b)

2.Simplification

The cube of the sum of two terms is the total of the cubes of the two terms plus three times the product of the two terms added together. a3+ b3 + 3ab(a+b)=(a + b)3

Examples

Example 1 - Solve (2 + 3)3

Answer- We know the formula a3+ b3 + 3ab(a+b)=(a + b)3

So here a = 2 and b = 3

So we will put these values in the formula, after putting the values we will get-

23+ 33 + 3*2*3*(2+3)=(2 + 3)3

= 8+27+18 *5

=8+27+90

=125

Hence, 125 is the answer.

Example 2 - Solve (1e + 2d)3

Answer- We know the formula a3+ b3 + 3ab(a+b)=(a + b)3

So here a = 1e and b = 2d

So we will put these values in the formula, after putting the values we will get-

(1e)3+ (2d)3 + 3*1e*2d*(1e+2d)=(1e + 2d)3

= e3+8d3+6ed *(1e+2d)

=e3+8d3+6e2d+12ed2

Hence, e3+8d3+6e2d+12ed2 is the answer.

Example 3 - Solve (3h + i)3

Answer- We know the formula a3+ b3 + 3ab(a+b)=(a + b)3

So here a = 3h and b = i

So we will put these values in the formula, after putting the values we will get-

(3h)3+ i3 + 3*3h*i*(3h+i)=(3h + i)3

= 27h3+i3+9hi *(3h+i)

=27h3+i3+27h2i+9hi2

Hence , 27h3+i3+27h2i+9hi2 is the answer.

Proofs

The following two distinct mathematical techniques can be used to demonstrate the algebraic identity of a plus b for the full cube.

1. Algebraic approach

It is beneficial to use the product of three sum basis binomials to get the expansion of the a plus b whole cube formula.

2. Geometric approach

A cube's volume can be used to graphically demonstrate how the algebraic identity for a plus b entire cube can be expanded.