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The (a -b)^3formula is used lớn find the cubeof a binomial. This formula is also used khổng lồ 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 lớn calculate the cube of the difference of two terms very easily & 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.

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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 và 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 khổng lồ 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 nguồn 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 và simplify.