Question

Which expression represents a quadratic equation in two variables?

a) x(1,4x - 3,5y)
b) xy( x2 - xy + y2)
c) (1 + 2x - x2)5x
d) 3y2(2y - 1) + y - y(1 - y + y2) - y2 + y;

Answer 1

The expression that represents a quadratic equation in two variables is xy(x^2 - xy + y^2). the correct option is B.

Step-by-step explanation:

The expression that represents a quadratic equation in two variables is b) xy(x^2 - xy + y^2).

A quadratic equation in two variables is of the form ax^2 + bxy + cy^2 + dx + ey + f = 0. In this expression, the term xy(x^2 - xy + y^2) has both x and y raised to the power of 1, making it a quadratic expression. It represents a quadratic equation in two variables.

Answer 2

The expression that represents a quadratic equation in two variables is option B: xy(x^2 - xy + y^2).

Step-by-step explanation:

Definition of a Quadratic Equation in Two Variables:

A quadratic equation in two variables typically has a term involving the square of one or both variables.

Analysis of Each Option:

a) x(1,4x - 3,5y): Not quadratic, no squared terms.

b) xy(x^2 - xy + y^2): Quadratic, contains x^2 and y^2.

c) (1 + 2x - x^2)5x: Not quadratic, no y terms.

d) 3y^2(2y - 1) + y - y(1 - y + y^2) - y^2 + y: Not quadratic, no x^2 terms.

Therefore, the correct expression representing a quadratic equation in two variables is option B: xy(x^2 - xy + y^2).