Find the square of: 2a+b

In the Number system, there are various questions in which squares and square roots of the numbers are used to get the desired goal or to make the question convenient to solve. It is not only square and square roots, there are cubes and cube roots, and so on. There are direct methods of finding out the values, along with that, there are certain formulas derived to find the values. In this article let’s study how to find the square of a number.

Square

Square is simply a multiplication of a number twice with itself like the square of the mobile phone will be two mobile phones. Finding squares and square roots is a part of algebra in which algebraic identities are simplified. By using algebraic identities we can find the value of any question with ease, here properties are used to find the square of numbers however this is a basic level question in this domain. But further, there are some more questions of this domain which will also involve these basic identities to solve typical ones. Let’s take a look at the Basic Identities,

 (a + b)² = (a² + b² + 2ab)

(a + b + c)²= a² + b² + c² + 2ab + 2bc + 2ac

So, let’s solve the question

Find the square of  2a+b

There are three methods to find the square of 2a+b. The first method involves simple multiplication and using the square of any number, the second method involves using the identity based on the number of terms given in the question, the identity regarding that is used, the third method involves first splitting the expression and then using the property.

1^st Method- Simple multiplication of both the brackets

(2a+b)²

(2a+b)(2a+b)

On multiplying both the brackets

we get,  2a×2a + 2a×b + b×2a + b×b

 4a²+2ab+2ab+b²

4a²+4ab+b²

2^nd  Method- Using the identity

(2a+b)²

(2a)² + (b)² + 2×2a×b 

 { By using the property (a+ b)² = a²+b²+2ab }

4a²+b²+4ab

3^rd Method- Splitting and then application of the property

(2a+b)²

Here we can write (2a+b) as (a+ a+ b)

so, the question has become (a+ a+ b)²

(a)² + (a)² + (b)² + 2×a×a + 2×a×b + 2×b×a        

{ By using the property (a+ b+ c)² = a²+b²+c²+2ab+2bc+2ca }

a²+a²+b²+2a²+2ab+2ba

4a²+b²+4ab

Similar Questions

Question 1: Find the square of 5x-3y.

Solution:

(5x-3y)²

(5x-3y)(5x-3y)

25x²-15xy-15yx+9y²

25x²-30xy+9y²

Question 2: Find the square of 3a+7b.

Solution:

(3a+7b)²

(3a)²+(7b)²+2×3a×7b

9a²+14b²+42ab