(a+b)² =?
Please give step by step explaination.
Answers
(a+b)² =?
Calculate the Area of a Square
In this step, we evaluate the area of a square in algebraic form.
Proof of
formula in Geometrical Method
Math DoubtsAlgebraidentitiesSpecial Binomials Product
The expansion of the algebraic identity a plus b whole square can be derived in mathematical form by the geometrical approach. In this method, the concept of the areas of the geometrical shapes squares and rectangles are used in proving the a plus b whole square formula.
Calculate the Area of a Square
In this step, we evaluate the area of a square in algebraic form.
a plus b whole square
Take a square and divide it into two different parts vertically. The lengths of them are and respectively.
Similarly, divide the square horizontally with same lengths. So, the widths of them are also a and b respectively.
The length and width of the square are same and the length of its each side is a+b. Therefore, the area of the square is (a+b)×(a+b)
geometrically.Find the Areas of Geometric shapes
This geometrical procedure splits a square as four geometric shapes, in which two of them are different squares and remaining two are two rectangles. Now, evaluate the area of each geometrical shape in mathematical form.
Now, add areas of the all four geometrical shapes to express the whole area in mathematical form
According to the commutative property of multiplication, the product of a and b is equal to the product of b and a. The equality of the areas of both rectangles can also be proved geometrically.
Therefore, the term ba can be written as ab and vice-versa.
a²+ab+ab+b²
a²+b²+2ab
therefore,(a+b)²=a²+b²+2ab
see the image above you can get clarity about it ..........
Hope it's helped you.........
It is my opinion only..........
Mark me as brainliest if you can.......
Answer:
a²+2ab+b²
Step-by-step explanation:
a(a+b)+b(a+b)
=a²+ab+b²+ab
=a²+2ab+b²
Mark it as the Brainliest Answer