What is expand (t^2+2it^3-t^4+1)(1+2it) ?

The solution to expand (t^2+2it^3-t^4+1)(1+2it) is (t^2-5t^4+1)+(4t^3-2t^5+2t)i

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expand (t^2+2it^3-t^4+1)(1+2it)

expand

(t^{2} + 2 i t^{3} - t^{4} + 1) (1 + 2 i t)

(t^{2} - 5 t^{4} + 1) + (4 t^{3} - 2 t^{5} + 2 t) i

Solution steps

(t^{2} + 2 i t^{3} - t^{4} + 1) (1 + 2 i t)

Distribute parentheses

= t^{2} \cdot 1 + t^{2} \cdot 2 i t + 2 i t^{3} \cdot 1 + 2 i t^{3} \cdot 2 i t - t^{4} \cdot 1 - t^{4} \cdot 2 i t + 1 \cdot 1 + 1 \cdot 2 i t

Simplify

t^{2} \cdot 1 + t^{2} \cdot 2 i t + 2 i t^{3} \cdot 1 + 2 i t^{3} \cdot 2 i t - t^{4} \cdot 1 - t^{4} \cdot 2 i t + 1 \cdot 1 + 1 \cdot 2 i t : t^{2} + 4 t^{3} i - 5 t^{4} - 2 t^{5} i + 1 + 2 t i

= t^{2} + 4 t^{3} i - 5 t^{4} - 2 t^{5} i + 1 + 2 t i

Rewrite in standard complex form:

(t^{2} - 5 t^{4} + 1) + (4 t^{3} - 2 t^{5} + 2 t) i

= (t^{2} - 5 t^{4} + 1) + (4 t^{3} - 2 t^{5} + 2 t) i

π (9 - y)^{2}

(\frac{x}{4} + 3 y) (\frac{x}{4} + 2 y)

(900 - 0.01 x ln (x)) x

2 y - \frac{( 3 x ^{2} + 2 ) x ^{3} + 2 y}{2 x ^{3} + 4 y}

(- \frac{1}{8} + \frac{3}{8} x)^{2}

What is expand (t^2+2it^3-t^4+1)(1+2it) ?
The solution to expand (t^2+2it^3-t^4+1)(1+2it) is (t^2-5t^4+1)+(4t^3-2t^5+2t)i