Square of The Sum of Two Binomials

How to find the square of the sum of two binomials?

(a + b) (a + b) = a(a + b) + b(a + b)

                     = a² + ab + ba + b²

                     = a² + 2ab + b²

                     = a² + b²+ 2ab

Therefore, (a + b)² = a² + b² + 2ab

Square of the sum of two terms = square of 1^st term + square of 2^nd term + 2 × fist term × second term

This is called the binomial square.

It is stated as: the Square of the binomial (sum of two unlike term) is the square of the first term plus the square of the second term plus twice the product of two terms.

Worked-out examples on square of the sum of two binomials:

1. Expand (2x + 3y)², using suitable identity.

Solution:

We know, (a + b)² = a² + b² + 2ab

Here, a = 2x and b = 3y

= (2x)² + (3y)² + 2 (2x) (3y)

= 4x² + 9y² + 12xy

Therefore, (2x + 3y)² = 4x² + 9y² + 12xy.


2. Evaluate 105² using the formula of (a + b)².

Solution:

105² = (100 + 5)²

We know, (a + b)² = a² + b² + 2ab

Here, a = 100 and b = 5

(100 + 5)²

= (100)² + (5)² + 2 (100) (5)

= 10000 + 25 + 1000

= 11025

Therefore, 105² = 11025.


3. Evaluate (10.1)² using the identity.

Solution:

(10.1)² = (10 + 0.1)²

We know, (a + b)² = a² + b² + 2ab

Here, a = 10 and b = 0.1

(10 + 0.1)²

= (10)² + (0.1)² + 2 (10) (0.1)

= 100 + 0.01 + 2

= 102.01

Therefore, (10.1)² = 102.01.


4. Use the formula of square of the sum of two terms to find the product of (1/5 x + 3/2 y) (1/5 x + 3/2 y).

Solution:

(1/5 x + 3/2 y) (1/5 x + 3/2 y) = (1/5 x + 3/2 y)²

We know that (a + b)² = a² + b² + 2ab

Here, a = 1/5 x and b = 3/2 y

= (1/5 x)² + (3/2 y)² + 2 (1/5 x) (3/2 y)

= 1/25 x² + 9/4 y² + 3/5 xy

Therefore, (1/5 x + 3/2 y) (1/5 x + 3/2 y) = 1/25 x² + 9/4 y² + 3/5 xy.

From the above solved problems we come to know square of a number means multiplying a number with itself, similarly, square of the sum of two binomial means multiplying the binomial with itself.

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