# 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.

Bạn đang xem: Ab 2

## 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

Want khổng lồ find complex math solutions within seconds?
Use our không tính phí online calculator lớn solve challenging questions. With xechieuve.com.vn, find solutions in simple và easy steps.

Book a không lấy phí Trial Class

## 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.

Xem thêm: Đọc Tập Cuối Conan Thám Tử Lừng Danh Tập Cuối Cùng, Thám Tử Lừng Danh Conan: Phần Cuối

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.

Xem thêm: Kể Về Một Người Thân Mà Em Yêu Quý Nhất (51 Mẫu), Top 18 Mẫu Kể Về Một Người Thân Của Em Hay Nhất

Firstlyobserve the pattern of the numbers whether thenumbers have whole ^2 as power nguồn 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.