The (a -b)^3formula is used to find the cubeof a binomial. This formula is also used to factorize some special types of trinomials. This formula is one of the algebraic identities. The (a-b)^3 formula is the formula for the cubeof the differenceof two terms. This formula is used to calculate the cube of the difference of two terms very easily and quickly without doing complicated calculations. Let us learn more about(a-b)^3 formula along with solved examples.

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What Is the (a -b)^3 Formula?

The (a-b)^3 formula is used to calculate thecubeof a binomial. The formula is also known as the cube of the difference between two terms. To find the formula of (a -b)3, we will just multiply (a -b)(a -b) (a -b).

(a -b)3=(a -b)(a - b)(a -b)

= (a2-2ab + b2)(a -b)

= a3- a2b -2a2b +2ab2+ ab2-b3

= a3-3a2b + 3ab2-b3

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

Therefore,(a -b)3formula is:

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



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Examples on(a -b)^3Formula

Example 1:Solve the following expression using (a -b)3formula:(2x -3y)3

Solution:

To find: (2x - 3y)3Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3= (2x)3-3× (2x)2× 3y + 3× (2x)× (3y)2-(3y)3= 8x3-36x2y + 54xy2-27y3

Answer: (2x -3y)3 = 8x3-36x2y + 54xy2-27y3

Example 2:Find the value of x3-y3if x -y = 5and xy = 2 using (a -b)3formula.

Solution:

To find: x3-y3Given:x -y = 5xy = 2Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3Here, a = x; b = yTherefore,(x -y)3= x3-3×x2× y+ 3 × x× y2-y3 (x -y)3= x3-3x2y + 3xy2-y353=x3-3xy(x -y) -y3125= x3-3× 2× 5- y3x3-y3= 95

Answer: x3-y3= 95

Example 3:Solve the following expression using (a -b)3formula:

(5x - 2y)3

Solution:

To find: (5x - 2y)3Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3= (5x)3-3× (5x)2× 2y + 3× (5x)× (2y)2-(2y)3= 125x3-150x2y + 60xy2-8y3

Answer: (5x -2y)3 = 125x3-150x2y + 60xy2-8y3


FAQs on (a -b)^3Formula

What Is the Expansion of (a -b)3Formula?

(a -b)3formula is read as a minus b whole cube. Its expansion is expressed as(a -b)3=a3-3a2b + 3ab2-b3

What Is the(a -b)3Formula in Algebra?

The (a -b)3formula is also known as one of the importantalgebraic identities. It is read as aminus b whole cube. Its (a -b)3formula is expressed as(a -b)3=a3-3a2b + 3ab2-b3How To Simplify Numbers Usingthe(a -b)3Formula?

Let us understand the use of the (a -b)3formula with the help of the following example.Example:Find the value of (20- 5)3using the (a -b)3formula.To find:(20- 5)3Let us assume that a = 20 and b = 5.We will substitute these in the formula of(a- b)3.(a -b)3=a3-3a2b + 3ab2-b3(20-5)3= 203 - 3(20)2(5) + 3(20)(5)2- 53= 8000 - 6000 + 1500 - 125= 3375Answer:(20-5)3= 3375.

How To Use the(a -b)3Formula?

The following steps are followed while using(a -b)3formula.

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Firstlyobserve the pattern of the numbers whether thenumbers have whole ^3 as power or not.Write down the formula of(a -b)3(a -b)3=a3-3a2b + 3ab2-b3Substitute the values of a and b in the(a -b)3formula and simplify.