A + B Whole Square Formula and Its Use
This (a+b)2 formula is one of the algebraic identities which is used to find the square of a binomial
(a+b)2 Formula
Basics: This (a+b)2 formula is one of the algebraic identities which is used to find the square of a binomial. The (a+b)2 formula is used to find the square of the sum of two terms. The (a+b)2 formula is called identity as this formula is valid for every value of 'a' and 'b'. The 2 formulas are used to factorize the binomial. The explanations with examples of the formula (a+b)2 are given below.
Explanation of (a+b)2 Formula
The algebraic identity is used to find the square of binomials. To find the formula, we will first write
(a+b)2= (a + b)(a + b)
By using binomial multiplication
(a+b)2 = a2 + ab + ba + b2
(a+b)2 = a2+ 2ab + 2
Therefore, (a + b)2 = a2 + 2ab + b2
Examples based on the (a+b)2 formula are given below
Example 1: Find the value of (3x + 7y)2 using (a + b)2 formula.
Solution:
To find: The value of (2x + 7y)2.
Let us assume that a = 2x and b = 7y.
(a + b)2 = a2 + 2ab + b2
(2x+3y)2 =(2x)2 + 2(2x)(7y) +(7y)2
= 4x2+28xy+49y2
Answer: (3x + 7y)2 = 4x2+ 28xy + 49y2.
Example 2: Factorize 4x2 + 4xy + y2 using (a + b)2 formula.
Solution:
To factorize: 4x2 + 4xy + y2.
The expression can be written as: (2x)2 + 2 (2x) (y) + (y)2.
a2 + 2ab + b2 = (a + b)2
Substitute a = 2x and b = y in this formula:
(2x)2 + 2 (2x) (y) + (y)2. = (2x + y)2
Answer: 4x2 + 4xy + y2 = (2x + y)2.
Example 3: Find the value of (30 + 5)2 using the (a + b)2 formula.
To find: (30+5)2
Let us assume that a = 30 and b = 5.
We will substitute these values in the formula of (a + b)2.
(a + b)2 = a2 + 2ab + b2
(30+5)2 = 900+ 2(30)(5) + 25
= 900 + 300 + 25
= 1225
Answer: (30 + 5)2 = 1225
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Frequently Asked Questions on A plus B Whole Square
. How to write the Expansion of (a + b)2 Formula?
The algebraic identity is used to find the square of binomials. To find the formula, we will first write
(a+b)2= (a + b)(a + b)
Now we can multiple one by one to get the right expression of (a+b)2
(a+b)2 = a2 + ab + ba + b2
Therefore, (a + b)2 = a2 + 2ab + b2
. A Plus B Whole Square Formula Proof
A plus B whole square formula can be proved by using a square. let's take a square with side “a” such that its area will be “a2”.you can extend the lengths of the square by b units such that we get two rectangles for more clarity just draw the diagram and try to write down this, and a small square with side b.
We can say the Side of the new square is now = a + b
Area can be written as = (a + b)2
Area of vertical strip can be written as = Length × Breadth = a × b = ab
Area of horizontal strip can be written as = Length × Breadth = a × b = ab
Area of smaller square = b2
Area of square with side (a +b) = Area of square with side “a” + Areas of two rectangles + Area of small square
(a + b)2 = a2 + ab + ab + b2
Therefore, (a + b)2 = a2 + 2ab + b2