Ask a New Question
Menu

Which of the following expressions are equivalent to 5a + 2b – 3c?

A.
a(4 + 2b) – 3c
B.
4a + (a + 2b) – 3c
C.
4a + 2(a + b) – 3c
D.
a + 4(a + b) – 2b – 3c

1 answer

To determine which expressions are equivalent to \( 5a + 2b - 3c \), we will simplify each option and see if it matches the target expression.

A. \( a(4 + 2b) – 3c \)

  1. Distribute \( a \): \[ a(4 + 2b) = 4a + 2ab \]
  2. Now, substitute back into the expression: \[ 4a + 2ab - 3c \] This does not match \( 5a + 2b - 3c \).

B. \( 4a + (a + 2b) – 3c \)

  1. Combine like terms: \[ 4a + a + 2b - 3c = 5a + 2b - 3c \] This matches \( 5a + 2b - 3c \) perfectly.

C. \( 4a + 2(a + b) – 3c \)

  1. Distribute \( 2 \): \[ 2(a + b) = 2a + 2b \]
  2. Now, substitute back into the expression: \[ 4a + 2a + 2b - 3c = 6a + 2b - 3c \] This does not match \( 5a + 2b - 3c \).

D. \( a + 4(a + b) – 2b – 3c \)

  1. Distribute \( 4 \): \[ 4(a + b) = 4a + 4b \]
  2. Substitute back into the expression: \[ a + 4a + 4b - 2b - 3c = 5a + 2b + 4b - 2b - 3c = 5a + 2b + 2b - 3c \] Which simplifies to: \[ 5a + 2b + 4b - 3c = 5a + 2b - 3c \] This does not match \( 5a + 2b - 3c \).

Conclusion

Only option B is equivalent to \( 5a + 2b - 3c \).