The (a -b)2formula is offered to uncover the square that a binomial.This (a -b)2formula is among the algebraic identities. This formula is likewise known together the formula because that the square that the difference of two terms. The(a -b)2formula is used to factorize some special species of trinomials. In this formula, wefind the square the the difference of 2 terms and thensolve it v the assist of algebraic identity. Let us learn an ext about(a -b)2formula together with solved examples in the following section.
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What Is(a-b)^2 Formula?
The (a -b)2formula is also widely known as the square that the difference between the two terms. This formula is occasionally used come factorizethe binomial. To discover the formula of(a -b)2, us will simply multiply (a -b)(a -b).
(a -b)2=(a -b)(a -b)
= a2-ab -ba + b2
= a2-2ab + b2
Therefore,(a -b)2formula is:
(a -b)2= a2-2ab + b2
Proof of(a − b)2Formula
Let united state consider(a - b)2as the area the a square with length (a - b). In the above figure, the biggestsquare is presented with areaa2.
To prove that (a -b)2= a2-2ab + b2, take into consideration reducing the length of all sides by variable b, and also it i do not care a - b. In the figure above, (a - b)2is displayed by the blue area.Now subtract the vertical and also horizontal strips that have actually the area a×b. Remove a × btwice will alsoremovethe overlapping square in ~ the bottom ideal cornertwice hence include b2. ~ above rearranging the data us have(a − b)2= a2− abdominal muscle − ab + b2. Hence this proves the algebraic identity(a − b)2= a2− 2ab + b2
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Examples on(a-b)^2 Formula
Let usconsider few illustrations based onthe (a-b)^2 formula in this solved instances section.
Example 1:Find the value of (x -2y)2by using(a -b)2formula.
To find: The value of (x - 2y)2.Let us assume that a = x and also b = 2y.We will substitute these worths in (a -b)2formula:(a -b)2= a2-2ab + b2(x-2y)2= (x)2-2(x)(2y) + (2y)2= x2- 4xy + 4y2
Answer:(x -2y)2= x2- 4xy + 4y2.
Example 2:Factorize x2- 6xy + 9y2by using(a -b)2formula.
To factorize: x2- 6xy + 9y2.We can write the given expression as:(x)2-2 (x) (3y) + (3y)2.Using(a -b)2formula:a2-2ab + b2=(a -b)2Substitute a = x and b = 3y in this formula:(x)2-2 (x) (3y) + (3y)2. = (x - 3y)2
Answer:x2- 6xy + 9y2= (x - 3y)2.
Example 3:Simplify the following using (a-b)2 formula.
(7x - 4y)2
a = 7x and also b = 4yUsing formula (a - b)2 =a2 - 2ab + b2(7x)2 - 2(7x)(4y) + (4y)249x2 - 56xy + 16y2
Answer:(7x - 4y)2=49x2 - 56xy + 16y2.
FAQs ~ above (a -b)^2Formula
What Is the growth of (a -b)2Formula?
(a -b)2formula is check out as a minusb entirety square. Its development is express as(a - b)2 =a2 - 2ab + b2
What Is the(a -b)2Formula in Algebra?
The (a -b)2formula is additionally known as among the importantalgebraic identities. It is check out as a minusb totality square. That (a -b)2formula is expressed as(a - b)2 =a2 - 2ab + b2
How To leveling Numbers Usingthe(a -b)2Formula?
Let us understand the usage of the (a -b)2formula with the aid of the complying with example.Example:Find the worth of (20- 5)2using the (a -b)2formula.To find:(20- 5)2Let us assume that a = 20 and b = 5.We will substitute this in the formula of(a- b)2.(a - b)2 =a2 - 2ab + b2(20-5)2= 202- 2(20)(5) + 52=400-200 + 25=225Answer:(20-5)2= 225.
How To use the(a -b)2Formula give Steps?
The adhering to steps are complied with while using(a -b)2formula.
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