Ab 2
The (a -b)2formula is used to 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 khổng lồ factorize some special types of trinomials. In this formula, wefind the square of the difference between two terms & 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. Khổng lồ 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
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 add 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 và 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 and 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 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 & 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 to lớn Use the(a -b)2Formula Give Steps?
The following steps are followed while using the (a -b)2formula.
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