What is taylor [(z-1)^3(z+1)^2] ?

The answer to taylor [(z-1)^3(z+1)^2] is -1+z+2z^2-2z^3-z^4

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taylor [(z-1)^3(z+1)^2]

taylor

[(z - 1)^{3} (z + 1)^{2}]

- 1 + z + 2 z^{2} - 2 z^{3} - z^{4}

Solution steps

Apply the Taylor Formula

= - 1 + \frac{\frac{d}{d z} ( [ ( z - 1 ) ^{3} ( z + 1 ) ^{2} ] ) ( 0 )}{1 !} z + \frac{\frac{d ^{2}}{d z ^{2}} ( [ ( z - 1 ) ^{3} ( z + 1 ) ^{2} ] ) ( 0 )}{2 !} z^{2} + \frac{\frac{d ^{3}}{d z ^{3}} ( [ ( z - 1 ) ^{3} ( z + 1 ) ^{2} ] ) ( 0 )}{3 !} z^{3} + \dots

Evaluate Derivatives

= - 1 + \frac{1}{1 !} z + \frac{4}{2 !} z^{2} + \frac{- 12}{3 !} z^{3} + \frac{- 24}{4 !} z^{4}

Refine

= - 1 + z + 2 z^{2} - 2 z^{3} - z^{4}

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What is taylor [(z-1)^3(z+1)^2] ?
The answer to taylor [(z-1)^3(z+1)^2] is -1+z+2z^2-2z^3-z^4