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Algebraic Expressions Problems

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1. Perform the indicated operation and simplify a. ሺ3π‘₯ βˆ’ 2ሻሺ4π‘₯ 3 + 2π‘₯ 2 βˆ’ 3π‘₯ሻ = ሺ3π‘₯ሻሺ4π‘₯ 3 ሻ + ሺ3π‘₯ሻሺ2π‘₯ 2 ሻ + ሺ3π‘₯αˆ»αˆΊβˆ’3π‘₯ሻ + αˆΊβˆ’2ሻሺ4π‘₯ 3 ሻ + αˆΊβˆ’2ሻሺ2π‘₯ 2 ሻ + αˆΊβˆ’2αˆ»αˆΊβˆ’3π‘₯ሻ = 12π‘₯ 4 + 6π‘₯ 3 βˆ’ 9π‘₯ 2 βˆ’ 8π‘₯ 3 βˆ’ 4π‘₯ 2 + 6π‘₯ = 12π‘₯ 4 βˆ’ 2π‘₯ 3 βˆ’ 13π‘₯ 2 + 6π‘₯ b. π‘₯ 2 βˆ’16 π‘₯ 2 +4π‘₯ = Γ· π‘₯ 2 βˆ’8π‘₯+16 π‘₯3 ሺπ‘₯ βˆ’ 4ሻሺπ‘₯ + 4ሻ π‘₯3 π‘₯2 βˆ™ = ሺπ‘₯ βˆ’ 4ሻሺπ‘₯ βˆ’ 4ሻ π‘₯ βˆ’ 4 π‘₯ሺπ‘₯ + 4ሻ 2. Factor the following completely: a. 3π‘₯ 3 βˆ’ 81 = 3ሺπ‘₯ 3 βˆ’ 27ሻ = 3ሺπ‘₯ 3 βˆ’ 33 ሻ 𝐴𝑝𝑝𝑙𝑦 π·π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ π‘œπ‘“ 𝐢𝑒𝑏𝑒𝑠 π‘“π‘œπ‘Ÿπ‘šπ‘’π‘™π‘Ž: π‘₯ 3 βˆ’ 𝑦 3 = ሺπ‘₯ βˆ’ π‘¦αˆ»αˆΊπ‘₯ 2 + π‘₯𝑦 + 𝑦 2 ሻ 3ሺπ‘₯ 3 βˆ’ 33 ሻ = 3ሺπ‘₯ βˆ’ 3ሻሺπ‘₯ 2 ...
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