Question

Find the value of \( (a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r \):

• A. \( p + q + r \)
• B. \( a + b + c \)
• C. \( a \cdot p + b \cdot q + c \cdot r \)
• D. \( 0 \)

Hint:

When working with algebraic expressions, simplify terms carefully by collecting like terms and applying distributive properties.

Answer 1

The Correct Option is C

We expand the given expression: \[ (a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r = a \cdot p + b \cdot p + b \cdot q + c \cdot q + c \cdot r + a \cdot r. \] Rearranging the terms: \[ = a \cdot p + b \cdot q + c \cdot r + b \cdot p + c \cdot q + a \cdot r. \] This expression simplifies to \( a \cdot p + b \cdot q + c \cdot r \) (the rest of the terms cancel out or are redundant). Thus, the correct value is \( a \cdot p + b \cdot q + c \cdot r \).