How To Find The Difference Of Cubes

Difference of Cubes Formula

The difference of cubes formula is used to discover the deviation of cubes of two numbers without actually calculating the cubes. It is one of the algebraic identities. The difference of cubes formula is used to factorize the binomials of cubes. The divergence of cubes formula is also known every bit aⁱⁱⁱ- b^three formula. The difference of cubes formula is explained beneath forth with solved examples in the following section.

What Is the Difference of Cubes Formula?

The difference of cubes formula or a³- b³ formula can be verified, by multiplying (a - b) (a² + ab + b²) and see whether you lot get a³ - b³.The difference of cubes formula is given as,

Divergence of Cubes Formula

a³- bⁱⁱⁱ= (a - b) (aⁱⁱ + ab + bⁱⁱ)

You lot can recall these signs using the post-obit trick.

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Examples Using Difference of Cubes Formula

Example 1:Find the value of 108³ - eight³by using the divergence of cubes formula.

Solution:

To find: 108³ - viii^three.

Let us assume that a = 108 and b = eight.

Nosotros will substitute these in the formula of deviation of cubes.

aⁱⁱⁱ- b³= (a - b) (a² + ab + bⁱⁱ)

108³−8^three= (108 − viii)(108²+ (108)(8) + viii²) = (100)(11664 + 864 + 64) = (100)(12592) = 1259200

Answer: 108^three - viii³ = ane,259,200.

Example 2:Factorize the expression 27x³ - 125 by using the difference of cubes formula.

Solution:

To factorize: 27x³ - 125.

We volition apply the divergence of cubesformula to factorize this.

We can write the given expression as

27xⁱⁱⁱ - 125 = (3x)^three - 5³

We will substitute a = 3x and b = 5 in the formula of the divergence of cubes.

a³- bⁱⁱⁱ= (a - b) (a^two + ab + bⁱⁱ)

(3x)³− 5³= (3x − 5)((3x)²+ (3x)(v) + five²) = (3x − 5)(9x² + 15x + 25)

Respond:27x³ - 125 = (3x - 5)(9x^two + 15x + 25).

Source: https://www.cuemath.com/difference-of-cubes-formula/

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