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The (a -b)2formula is used lớn find the square of a binomial.This a minus b Whole Square Formula is one of the commonly used algebraic identities. This formula is also known as the formula for the square of the difference between two terms. The(a -b)2formula is used to factorize some special types of trinomials. In this formula, wefind the square of the difference between two terms and thensolve it with the help of algebraic identity. Let us learn more abouta minus b Whole Squarealong 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 of the difference between the two terms. This formula is sometimes used lớn factorizethe binomial. To find the formula of(a -b)2, we will just 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 ofA minus B Whole Square Formula

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Let us consider(a - b)2as the area of a square with length (a - b). In the above figure, the biggestsquare is shown with areaa2.

To prove that (a -b)2= a2-2ab + b2, consider reducing the length of all sides by factor b, và it becomes a - b. In the figure above, (a - b)2is shown by the blue area.Now subtract the vertical and horizontal strips that have the area a×b. Removing a × btwice will alsoremovethe overlapping square at the bottom right cornertwice hence địa chỉ b2. On rearranging the data we have(a − b)2= a2− ab − 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 a few illustrations based onthe (a-b)^2 formula in this solved examples section.

Example 1:Find the value of (x -2y)2by using the (a -b)2formula.

Solution:

To find: The value of (x - 2y)2.Let us assume that a = x & b = 2y.We will substitute these values 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 aminus bWhole Square Formula.

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Solution:

To factorize: x2- 6xy + 9y2.We can write the given expression as:x2- 6xy + 9y2= (x)2-2 (x) (3y) + (3y)2.Using(a -b)2formula:a2-2ab + b2=(a -b)2Substitute a = x & 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

Solution:

a = 7x và 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 on A minus B Whole Square Formula

What Is the Expansion of (a -b)2Formula?

(a -b)2formula is read as a minusb whole square. Its expansion is expressed as(a - b)2 =a2 - 2ab + b2

What Is the(a -b)2Formula in Algebra?

The (a -b)2formula is also known as one of the importantalgebraic identities. It is read as a minusb whole square. Its (a -b)2formula is expressed as(a - b)2 =a2 - 2ab + b2

How to lớn Simplify Numbers UsingtheA minus B Whole Square Formula?

Let us understand the use of the (a -b)2formula with the help of the following example.Example:Find the value of (20- 5)2using the (a -b)2formula.To find:(20- 5)2Let us assume that a = 20 and b = 5.We will substitute these 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 khổng lồ Use the(a -b)2Formula Give Steps?

The following steps are followed while using the (a -b)2formula.

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Firstlyobserve the pattern of the numbers whether thenumbers have whole ^2 as power or not.Write down the formula of(a -b)2(a - b)2 =a2 - 2ab + b2substitute the values ofa và b in the(a -b)2formula & simplify.