The (a -b)^3formula is supplied to uncover the cubeof a binomial. This formula is additionally used to factorize some special types of trinomials. This formula is among the algebraic identities. The (a-b)^3 formula is the formula for the cubeof the differenceof 2 terms. This formula is offered to calculate the cube that the difference of 2 terms an extremely easily and quickly there is no doing facility calculations. Let us learn an ext about(a-b)^3 formula together with 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 additionally known as the cube that the difference between two terms. To find the formula the (a -b)3, us 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 adhering to expression using (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 making use of (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 expansion of (a -b)3Formula?
(a -b)3formula is read as a minus b whole cube. Its development 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 among the importantalgebraic identities. That is read as aminus b whole cube. That is (a -b)3formula is express as(a -b)3=a3-3a2b + 3ab2-b3How To simplify Numbers Usingthe(a -b)3Formula?
Let us understand the usage of the (a -b)3formula v the assist of the adhering to 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 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 usage the(a -b)3Formula?
The complying with steps are followed while using(a -b)3formula.
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