Find the square of: 3a+7b

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 a 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 the value of any question can be found with ease, here use properties to find the square of numbers however this is a basic level question in this domain. But further, some more questions of this domain will also involve these basic identities to solve typical ones, those questions are easier to solve with the help of 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 3a+7b.

There are three methods to find the square of 3a+7b. 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.

1st Method- Simple multiplication of both the brackets

(3a+7b)²

(3a+7b)(3a+7b)

On multiplying both the brackets

It is obtained,  3a×3a + 3a×7b + 7b×3a + 7b×7b

9a²+21ab+21ab+49b²

9a²+42ab+49b²

2nd  Method- Using the identity

(3a+7b)²

(3a)² + (7b)² + 2×3a×7b      

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

 9a²+49b²+42ab

3rd Method- Splitting and then application of the property

(3a+7b)²

Here we can write (3a+7b) as (2a+a+7b)

So, the question has become (2a+a+7b)²

(2a)² + (a)² + (7b)² + 2×2a×a + 2×a×7b + 2×7b×2a         

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

4a²+a²+49b²+4a²+14ab+28ba

9a²+49b²+42ab

Similar Questions

Question 1:  Find the square of 5x-y.

Solution:

(5x-y)²

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

25x²-5xy-5yx+y²

25x²-10xy+y²

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

Solution:

(a+2b)²

(a)²+(2b)²+2×a×2b

a²+4b²+4ab