A plus B Whole Square

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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A plus B Whole Square
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A plus B Whole Square

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Frequently Asked Questions on A plus B Whole Square

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 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