A Cube Plus B Cube Formula | a^3 + b^3 Formula

The addition of cubes (of the two specified numbers) formula is called as the (a3+b3) formula. Without computing the two cubes, the sum can be calculated using the a cube plus b cube formula. The binomials of cubes are factorised using it as well.

a cube plus b cube Formula

The formula for "a cube + b cube" is written below:

The equation is (a + b)(a2- ab + b2)=a3+b3.

a cube plus b cube identity is another claim made for it.

The Proof of “a” cube plus “b” cube formula

By using the formula (a + b)3, we can determine that

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

We obtain (a + b) by subtracting 3ab (a + b) from both sides.

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

By taking (a + b) as common, we obtain

a3 + b3= [(a + b)2 – 3ab](a + b)

The above-mentioned statement can be written as follows:

(a + b) [a2 + b2 + 2ab - 3ab]=a3+b3 (By identity: (a plus b)2=a2+b2+2ab)

Hence, the formula for a3+b3 is -

a3+ b3 = (a + b) * (a2 – a*b + b2)

Examples On a Cube Plus b Cube

Example 1: Solve y3+27.

Answer: We can write y3+27 as y3 + 33

Currently, y3 + 33 is represented by c3+ d3.

c3+ d3 = (c+ d)* (c2 – cd + d2) yields the following results:

y3+ 33 = (y + 3) (y2 – 3y + 32)

y3+27.00 = (y + 3.00)* (y2 – 3y + 9.00)

Example 2: Prove that the c3+ d3 formula is valid for i3+(2j)3.

Answer: We know the formula -

c3+ d3 = (c+ d)* (c2 – cd + d2)

So here c=i and d = 2j

So when we will put the values in the equation, we will get-

i3+ (2j)3 = (i+ 2j)* (i2 – i*2j + (2j)2)

Here LHS is i3+ (2j)3

Solving RHS

= (i+ 2j)* (i2 – 2ij + 4j2)

= i3-2i2j+4ij2+2i2j-4ij2+8j3

=i3+8j3

It can be written as i3+ (2j)3.

Hence LHS=RHS

Therefore, The formula is valid for i3+(2j)3.

a+b whole cube

The cube of a binomial is calculated using the (a+b)3 formula. Some particular varieties of trinomials can also be factored in using this technique. This formula is included in the algebraic identities as well.

The equation for the cube of a two-term sum.

a3 + 3*a2*b + 3*a*b2 + b3=(a+b)3

a+b whole cube formula

One of the crucial algebraic identities is the (a+b)3 equation. A + B Whole Cube is how it should be read. The formula for (a+b)3 reads as follows a3 + 3*a2*b + 3*a*b2 + b3=(a+b)3

a minus b whole cube

The (a-b)3formula, also known as the (a-b) the whole cube formula is used to calculate the cube of the difference between two terms. Some varieties of trinomials can also be factored using this technique. One of the crucial algebraic identities is the formula for the (a-b) entire cube. In most cases, the problems are quickly solved using the (a-b)3 formula without the need for laborious calculations.

a3 - 3 *a2*b + 3*a *b2 - b3 = (a - b)3

a minus b whole power 4

a minus b whole power 4-

a4 + b4 - 4a3 b + 6a2 b2- 4ab3=(a-b)4