The (a -b)^3formula is offered to discover the cubeof a binomial. This formula is likewise used to factorize some special varieties 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 distinction of two terms really easily and quickly without doing facility calculations. Let united state learn an ext about(a-b)^3 formula in addition to solved examples.
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What Is the (a -b)^3 Formula?
The (a-b)^3 formula is offered to calculate thecubeof a binomial. The formula is also known as the cube of the difference between two terms. To find the formula the (a -b)3, we will simply 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 complying with expression making use of (a -b)3formula:(2x -3y)3
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 worth of x3-y3if x -y = 5and xy = 2 using (a -b)3formula.
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 complying with expression utilizing (a -b)3formula:
(5x - 2y)3
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 development of (a -b)3Formula?
(a -b)3formula is check out as a minus b entirety cube. Its growth is express as(a -b)3=a3-3a2b + 3ab2-b3
What Is the(a -b)3Formula in Algebra?
The (a -b)3formula is additionally known as one of the importantalgebraic identities. It is review as aminus b whole cube. Its (a -b)3formula is express as(a -b)3=a3-3a2b + 3ab2-b3How To leveling Numbers Usingthe(a -b)3Formula?
Let us understand the usage 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 also b = 5.We will substitute this 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 usage the(a -b)3Formula?
The adhering to steps are followed while using(a -b)3formula.
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