Question

Select all that are like terms to 4x^3y^2.

a) 3x^2y^3
b) 4x^3y^3
c) −4x^2y^3
d) −2x^3y^2
e) −4x^2y
f) x^3y^2
g) 6x^3y^2

Answer 1

The like terms to 4x^3y^2 are: a) 3x^2y^3, c) −4x^2y^3, e) −4x^2y, and g) 6x^3y^2.

Step-by-step explanation:

Like terms share the same base (combination of variables raised to their respective exponents) with potentially different coefficients and signs. We analyze each option:

a) 3x^2y^3: Shares the base x^3y^2 with a different coefficient (3 vs. 4).

b) 4x^3y^3: Shares the base but has a different exponent in the y term (y^3 vs. y^2).

c) −4x^2y^3: Shares the base with a different coefficient and sign (-4 vs. 4).

d) −2x^3y^2: Shares the base but has a different coefficient (-2 vs. 4).

e) −4x^2y: Shares the base x^2y with a different coefficient and sign (-4 vs. 4).

f) x^3y^2: Shares the base but has a different coefficient (1 vs. 4).

g) 6x^3y^2: Shares the base with a different coefficient (6 vs. 4).

Therefore, options a), c), e), and g) are like terms to 4x^3y^2 because they share the same variable combination raised to the same powers, with variations only in coefficients and signs.