. Simplify: (2p – 3q)(p^2 + q^2 + pq) – (p – 3q)(4p + q + 9pq)

asked by guest
on Dec 08, 2024 at 1:58 am



You asked:

Simplify the expression: \(\left(2 p - 3 q\right) \left({p}^{2} + {q}^{2} + p q\right) - \left(p - 3 q\right) \left(4 p + q + 9 p q\right)\)

MathBot Answer:

Expanded:

\[ \left(2 p - 3 q\right) \left({p}^{2} + {q}^{2} + p q\right) - \left(p - 3 q\right) \left(4 p + q + 9 p q\right) = 2 p^{3} - 10 p^{2} q - 4 p^{2} + 26 q^{2} p + 11 p q - 3 q^{3} + 3 q^{2} \]

Factored:

\[ \left(2 p - 3 q\right) \left({p}^{2} + {q}^{2} + p q\right) - \left(p - 3 q\right) \left(4 p + q + 9 p q\right) = 2 p^{3} - 10 p^{2} q - 4 p^{2} + 26 q^{2} p + 11 p q - 3 q^{3} + 3 q^{2} \]


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