\dfrac{z^8+11z^4+30}{18z^2+12z+2} \cdot \dfrac{24z^2+8z}{z^2+6z}=

asked by guest
on Nov 23, 2024 at 5:48 pm



You asked:

Evaluate the expression: \(\frac{{z}^{8} + 11 {z}^{4} + 30}{18 {z}^{2} + 12 z + 2} \cdot \frac{24 {z}^{2} + 8 z}{{z}^{2} + 6 z}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{z}^{8} + 11 {z}^{4} + 30}{18 {z}^{2} + 12 z + 2} \cdot \frac{24 {z}^{2} + 8 z}{{z}^{2} + 6 z} = \frac{\left(24 z^{2} + 8 z\right) \left(z^{8} + 11 z^{4} + 30\right)}{\left(z^{2} + 6 z\right) \left(18 z^{2} + 12 z + 2\right)} \)

Expanded

\[\frac{{z}^{8} + 11 {z}^{4} + 30}{18 {z}^{2} + 12 z + 2} \cdot \frac{24 {z}^{2} + 8 z}{{z}^{2} + 6 z} = \frac{24 z^{10}}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z} + \frac{8 z^{9}}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z} + \frac{264 z^{6}}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z} + \frac{88 z^{5}}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z} + \frac{720 z^{2}}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z} + \frac{240 z}{18 z^{4} + 120 z^{3} + 74 z^{2} + 12 z}\]

Factored

\[\frac{{z}^{8} + 11 {z}^{4} + 30}{18 {z}^{2} + 12 z + 2} \cdot \frac{24 {z}^{2} + 8 z}{{z}^{2} + 6 z} = \frac{4 \left(z^{4} + 5\right) \left(z^{4} + 6\right)}{\left(3 z + 1\right) \left(z + 6\right)}\]

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