simplify (3t+2it)^2

Solution

simplify

(3 t + 2 i t)^{2}

5 t^{2} + 12 t^{2} i

Solution steps

(3 t + 2 i t)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(3 t + 2 i t)^{2} = (3 t)^{2} + 2 \cdot 3 t \cdot 2 i t + (2 i t)^{2}

= (3 t)^{2} + 2 \cdot 3 t \cdot 2 i t + (2 i t)^{2}

Simplify

(3 t)^{2} + 2 \cdot 3 t \cdot 2 i t + (2 i t)^{2} : 5 t^{2} + 12 t^{2} i

= 5 t^{2} + 12 t^{2} i

\frac{3 x ^{2} + 6 x + 5}{( x + 2 ) ^{2}}

6 (7 + 5)

(5 - x)^{2}

\frac{10 ( x ^{2} - 1 )}{x ^{3}}

x (1 - x)