Example Question - distributing terms
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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
Simplifying an Algebraic Expression
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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