A student simplified the expression. Identify the errors and correct them.
3p^2*q+2p-(5q+p-2p^2*q)=q^2*p=3p-5q
The student made a few errors in simplifying the expression. Here are the corrections:
1) The expansion -(5q+p-2p^2*q) should be simplified correctly: -(5q + p) + 2p^2*q.
2) The expression on the left side, 3p^2*q + 2p - (5q + p) + 2p^2*q, is not simplified correctly. We combine like terms to simplify further.
3p^2*q + 2p - 5q - p + 2p^2*q
= 5p^2*q + p - 5q
3) The student wrote q^2*p instead of p^2*q on the right side of the equation.
The corrected equation is: 5p^2*q + p - 5q = p^2*q - 3p + 5q
Let's break down the expression and identify the errors:
Given expression: 3p^2*q + 2p - (5q + p - 2p^2*q) = q^2*p = 3p - 5q
1. The error in the given expression is the incorrect simplification of the terms. We need to simplify it correctly step by step.
Step 1: Distribute the negative sign inside the parentheses:
3p^2*q + 2p - 5q - p + 2p^2*q = q^2*p = 3p - 5q
Step 2: Combine like terms:
3p^2*q + 2p + 2p^2*q - 5q - p = q^2*p = 3p - 5q
Step 3: Combine the similar polynomial terms:
(3p^2*q + 2p^2*q) + (2p - p) - (5q - 5q) = q^2*p = 3p - 5q
Step 4: Simplify further:
5p^2*q + p - q = q^2*p = 3p - 5q
Step 5: Rearrange the terms:
5p^2*q + p - q = 3p - 5q = q^2*p
2. There is another error in the given expression, specifically in the last part where it states "3p - 5q = q^2*p." This is incorrect.
Corrected expression:
5p^2*q + p - q = q^2*p
Please note that without more specific instructions, we cannot solve the equation for the variables p and q.