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.

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

Now let us see the

**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

**(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**

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