FORMULA FOR A PLUS B WHOLE SQUARE

On this webpage formula for a plus b whole square, that is (a+b)²  we are going to see some example problems based on this formula.

What is Algebraic identity?

An identity is an equality that remains true regardless of the values of any variables that appear within it.

Now let us see the

formula for a plus b whole square

Question 1 :

Expand (5x + 3)²

Solution:

Here the given question is in the form of (a+b)². Instead of a we have "5x" and instead of b we have "3" . So we need to apply the formula a² + 2ab + b ² and we need to apply those values instead of a and b

a = 5 x and b = 3

(5x + 3)² = (5x)² + 2 (5x) (3) + (3)²

               = 25x² + 30 x + 9

               = 25x² + 30 x + 9            


Question 2 :

Expand (x + 2) ²

Solution:

Here the question is in the form of (a+b) ². Instead of a we have "x" and instead of b we have "2" . So we need to apply the formula a² + 2ab + b ² and we need to apply those values instead of a and b

a = x   and b = 2

(x + 2)² = (x)² + 2 (x) (2) + (2)²

               = x² + 4 x + 4


Question 3 :

If a + b = 3 and a² + b² = 29,find the value of ab.

Solution:

In this problem to get the value of ab we can use the formula for a plus b whole square that is  (a + b)² = a² + b² - 2 a b

3² = 29 - 2ab

9 = 29 - 2 ab

2 a b = 29 - 9

2 a b = 20

ab = 20/2

 ab = 10


Question 4 :

 [√2 + (1/√ 2)]²  is equal to

Solution:

(a + b)² = a² + b² + 2 a b

a = √2  b = 1/√2

 [√2 + (1/√ 2)]² = ( √2 )² + (1/√2)² + 2 √2 (1/√2)

                         = 2 + (1/2) + 2

                         = 4 + (1/2) 

                         = 9/2


Question 5 :

 (105)²  is equal to

Solution:

Instead of multiplying 105 x 105 to get the value of (105)² we can use algebraic formula for a plus b whole square that is  (a+b)² to get the same answer.105 can be written as 100 + 5.

(105)² = (100 + 5)²

(a + b)² = a² + b² + 2 a b

a = 100  b = 5

 (105)² = (100)² + (5)² + 2 (100)(5)

             = 10000 + 25 + 1000

             = 11025

(a + b)² = a² + 2 ab + b²

(a - b)² = a² - 2 ab + b²

a² - b² = (a + b) (a - b)

(x+a)(x+b)=x²+(a+b)x+ab

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b+3ab²-b³

(a³+b³)= (a+b)(a²-ab+b²)

(a³-b³)=(a-b)(a²+ab+ b²)

(a+b+c)²= a²+b²+c²+2ab+2bc+2ca