My answer:
x^2+3xy+3x+2y^2-3y
Textbook Answer:
x^2+3xy+2y^2+3x-3y
Does the order matter? Thanks.
No. Does the answer to 2 + 3 differ from the answer for 3 + 2?
Actually, the answer does matter. When writing algebraic equations, you need to put the variables in order according to their exponents.
Yes, the order matters when it comes to writing the terms of a polynomial expression. In this case, the order of the terms has been rearranged between your answer and the textbook answer. While both expressions have the same set of terms, they are written in a different order.
To determine the correct order, it is important to follow a specific convention. The standard convention for ordering terms in a polynomial expression is to arrange them in descending order of the power of the variables. In other words, the terms with the highest powers of the variables are written first, followed by terms with lower powers.
In the given expression, we have terms with variables x and y, raised to different powers. To find the correct order, we need to identify the terms with the highest powers and write them first while keeping similar terms together.
Let us break down the given expression and identify the terms:
x^2 + 3xy + 3x + 2y^2 - 3y
Here, the term with the highest power of x is x^2, and the term with the highest power of y is 2y^2. So, those terms should be written first.
The next terms would include the ones with lower powers of x and y, which are 3xy, 3x, and -3y.
So, the correct order, following the standard convention, would be:
x^2 + 3xy + 2y^2 + 3x - 3y
Hence, the textbook answer x^2 + 3xy + 2y^2 + 3x - 3y is in the correct order, while your answer x^2 + 3xy + 3x + 2y^2 - 3y is not.