(3p-2q)(4p+8q)-1/2(2p+16q)(2p-16q)

asked by guest
on Nov 16, 2024 at 3:03 pm



You asked:

Evaluate the expression: (3p−2q)(4p+8q)−12(2p+16q)(2p−16q)\left(3 p - 2 q\right) \left(4 p + 8 q\right) - \frac{1}{2 \left(2 p + 16 q\right) \left(2 p - 16 q\right)}

MathBot Answer:

Evaluated



(3p−2q)(4p+8q)−12(2p+16q)(2p−16q)=(3p−2q)(4p+8q)−12⋅(2p−16q)(2p+16q)\displaystyle \left(3 p - 2 q\right) \left(4 p + 8 q\right) - \frac{1}{2 \left(2 p + 16 q\right) \left(2 p - 16 q\right)} = \left(3 p - 2 q\right) \left(4 p + 8 q\right) - \frac{1}{2 \cdot \left(2 p - 16 q\right) \left(2 p + 16 q\right)}

Expanded

(3p−2q)(4p+8q)−12(2p+16q)(2p−16q)=12p2+16pq−16q2−18p2−512q2\left(3 p - 2 q\right) \left(4 p + 8 q\right) - \frac{1}{2 \left(2 p + 16 q\right) \left(2 p - 16 q\right)} = 12 p^{2} + 16 p q - 16 q^{2} - \frac{1}{8 p^{2} - 512 q^{2}}

Factored

(3p−2q)(4p+8q)−12(2p+16q)(2p−16q)=96p4+128p3q−6272p2q2−8192q3p+8192q4−18(p−8q)(p+8q)\left(3 p - 2 q\right) \left(4 p + 8 q\right) - \frac{1}{2 \left(2 p + 16 q\right) \left(2 p - 16 q\right)} = \frac{96 p^{4} + 128 p^{3} q - 6272 p^{2} q^{2} - 8192 q^{3} p + 8192 q^{4} - 1}{8 \left(p - 8 q\right) \left(p + 8 q\right)}

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