Question - Simplifying an Algebraic Expression
Solution:
To simplify the expression $$ 3p(p - q) - (2p - q)^2 $$, follow these steps:Step 1: Distribute the $$3p$$ in the first term:\[ 3p^2 - 3pq \]Step 2: Expand the squared term $$(2p - q)^2$$:\[ (2p - q)(2p - q) = 4p^2 - 4pq + q^2 \]Step 3: Subtract the expanded squared term from the first term:\[ (3p^2 - 3pq) - (4p^2 - 4pq + q^2) \]Step 4: Distribute the negative sign across the terms in the parentheses:\[ 3p^2 - 3pq - 4p^2 + 4pq - q^2 \]Step 5: Combine like terms:\[ (3p^2 - 4p^2) + (-3pq + 4pq) - q^2 \]\[ -p^2 + pq - q^2 \]So, $$ 3p(p - q) - (2p - q)^2 = -p^2 + pq - q^2 $$.
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