Step-by-step explanation:
a. Combining like terms:
\[ x + x - 3 + 4x^2 + 2x - x = 6x + 4x^2 - 3 \]
b. Combining like terms:
\[ 8x^2 + 3x - 13x^2 + 10x^2 - 25x - x = 5x^2 - 19x \]
c. No like terms to combine:
\[ 4x + 3y \]
d. Combining like terms:
\[ 20 + 3xy - 3 + 4y^2 + 10 - 2y^2 = 30 + 3xy + 2y^2 \]
Step-by-step explanation:
a. Like terms are those with the same variable(s) raised to the same exponent(s). In this case, \( x \) is the common variable. Combining like terms involves adding or subtracting the coefficients of \( x \) and the constants separately.
b. Similar to the first case, \( x^2 \) terms can be combined by adding their coefficients, and \( x \) terms can also be combined.
c. \( 4x \) and \( 3y \) are not like terms because they involve different variables. Thus, they cannot be combined.
d. Like terms are \( 3xy \) and \( 2y^2 \) as they share the variable \( y \). \( 20 \), \( -3 \), \( 10 \), and \( -3 \) are constants and can be combined as well.