Math Guide

Square of the Sum of Two Numbers

Thesquare of the two numbers is said as perfect square. Let us take the two number a and b for adding. Thus,the expression of sum of the two number is (a + b). Now the expression of the square of the sum of two numbers is (a + b)2. Let see how to get the result of square of the sum of two numbers.


Expanded Form - Square of the Sum of Two Numbers:


Where a and b are two number, then expand form of the square of the sum of the two numbers is (a + b)2 = a2 + b2 + 2ab.


Example problem - Square of the Sum of Two Numbers:

Example 1:

What is the square of the sum of two numbers 3 and 5?

Solution:

Formula: (a + b)2 = a2 + b2 + 2ab.

(3 + 5)2 = 32 + 52 + 2 * 3 * 5

(3 + 5)2 = 9 + 25 + 30 = 64

(3 + 5)2 = 64

Answer: The Square of the sum of two numbers 3 and 5 is 64.


Another Method:


Step 1: First sum the given two number 3 and 5

3 + 5 = 8

Step 2: Square the sum of the given two numbers.

82 = 8 × 8 = 64

Answer: 64


Example 2:

What is the square of the sum of two numbers 4 and 7?

Solution:

Formula: (a + b)2 = a2 + b2 + 2ab.

(4 + 7)2 = 42 + 72 + 2 * 4 * 7

(4 + 7)2 = 16 + 49 + 56 = 121

(4 + 7)2 = 121

Answer: The Square of the sum of two numbers 4 and 7 is 121.


Another Method:

Step 1: First sum the given two numbers 4 and 7.

4 + 7 = 11


Step 2: Square the sum of the given two numbers.

112 = 11 × 11 = 121

Answer: 121


Practice Problem – Square of the Sum of Two Numbers:

1. What is the square of the sum of two numbers 4 and 9?

Answer: 169

2. What is the square of the sum of two numbers 2 and 7?

Answer: 81