To determine the like terms to \( 4x^3y^2 \), we need to focus on the variable parts of the terms, specifically the exponents of \( x \) and \( y \). Like terms must have the same variables raised to the same powers.
Let's analyze each given term:
1. \( x^2 y^3 \): The exponents are \( x^2 \) and \( y^3 \). These do not match the exponents in \( 4x^3y^2 \), which are \( x^3 \) and \( y^2 \).
2. \( 4x^3y^3 \): The exponents are \( x^3 \) and \( y^3 \). These also do not match with \( x^3 \) and \( y^2 \).
3. \( -4x^3y^2 \): The exponents are \( x^3 \) and \( y^2 \). These match exactly with the exponents in \( 4x^3y^2 \).
4. \( -2x^3y^2 \): The exponents are \( x^3 \) and \( y^2 \). These also match with the exponents in \( 4x^3y^2 \).
5. \( -4x^2y^2 \): The exponents here are \( x^2 \) and \( y^2 \). These do not match with the exponents \( x^3 \) and \( y^2 \).
6. \( x^3y^2 \): The exponents are \( x^3 \) and \( y^2 \). These match exactly with the exponents in \( 4x^3y^2 \).
7. \( 6x^3y^2 \): The exponents are \( x^3 \) and \( y^2 \). These also match with the exponents in \( 4x^3y^2 \).
So the like terms to \( 4x^3y^2 \) are:
- \( -4x^3y^2 \)
- \( -2x^3y^2 \)
- \( x^3y^2 \)
- [tex]\( 6x^3y^2 \)[/tex]
