Question

What is the difference between perfect square and difference of squares?

Answer 1

Hint: A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. For example ${5^2}$ is a perfect square of a real number, $5$.Difference of squares refers to the difference of two perfect square values. So, we will describe the differences between the two in a pointwise manner.

Complete answer:
The differences in the perfect squares and difference between the perfect squares are:

Perfect square	Difference of squares
A perfect square quadratic algebraic expression looks like ${a^2} - 2ab + {b^2}$ or ${a^2} + 2ab + {b^2}$.	The algebraic expression for the difference between the perfect square values looks like ${a^2} - {b^2}$.
The perfect square can be factored as ${\left( {a - b} \right)^2}$ or ${\left( {a + b} \right)^2}$.	The difference of square can be factored as $\left( {a + b} \right)\left( {a - b} \right)$ .
The result of the perfect square is the product of two like terms and can be factored into the constituent terms again. For example: $25 = {5^2} = 5 \times 5$	The result of the difference of two squares may or may not be expressed as a product of two like terms.For example: ${8^2} - {4^2} = 64 - 16 = 48$
Perfect square values are always positive or equal to zero. They cannot be non-negative.	Differences of squares may be positive, negative or zero depending upon the order of the numbers taken.
Perfect square values cannot have $2$, $3$, $7$ or $8$ at the unit's place.	Differences of squares may have $2$, $3$, $7$ or $8$ at the units place.

Note: We all know that when two negative or two positive numbers are multiplied to each other then the result will always be a positive number. Hence, the square values are always positive. We must know the properties of perfect squares to solve theoretical questions. We also must have a strong grip over the algebraic identities and concepts.