Question

Write whether the following statements are True or false. Justify your answer
The degree of \[{x^2} + 2xy + {y^2}\] is 2.
A. True
B. False

Answer 1

Hint:- Degree of the quadratic equation is the power of each term of the quadratic equation. Highest power of a variable is the degree of the polynomial.

Complete step-by-step answer:
As we know that the variable is a term which is not consistent or having a fixed pattern, liable to change or we can say that the variable is able to be changed or adapted.
So, the variables in the equation \[{x^2} + 2xy + {y^2}\] are x and y.
So, now we can see that the power of the first term \[{x^2}\] is 2. And the power of the term \[2xy\] is also 2 because the power of x in 2xy is 1 and the power of y in 2xy is also 1. So, 1 + 1 = 2.
And the power of the term \[{y^2}\] in the given equation is also 2.
So, we can see that the degree of each term in the given equation \[{x^2} + 2xy + {y^2}\] is 2.
Hence, the given statement is true.

Note:- Whenever we come up with this type of problem, we should remember that the degree of the constant term is zero because degree is only defined for variables. And the degree of any variable is the power of that variable like the degree of x is 1, degree of \[{x^2}\] is 2.