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**

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**