Example Question - expanding algebraic expressions

Expanding and Simplifying Algebraic Expressions

3p(p - q) - (2p - q)² Step 1: Distribute 3p in the first term = 3p² - 3pq Step 2: Expand the square in the second term = (2p - q)(2p - q) = 4p² - 2pq - 2pq + q² Step 3: Combine like terms in the second term = 4p² - 4pq + q² Step 4: Subtract the expanded second term from the first term = (3p² - 3pq) - (4p² - 4pq + q²) Step 5: Distribute the subtraction across each term in the parentheses = 3p² - 3pq - 4p² + 4pq - q² Step 6: Combine like terms = -p² + pq - q² The final answer: = -p² + pq - q²