# 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 + b² and we need to apply those values 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 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

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(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