simplify (5-3xi)^2

Solution

simplify

(5 - 3 x i)^{2}

(25 - 9 x^{2}) - 30 x i

Solution steps

(5 - 3 x i)^{2}

Apply Perfect Square Formula:

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

(5 - 3 x i)^{2} = 5^{2} - 2 \cdot 5 \cdot 3 x i + (3 x i)^{2}

= 5^{2} - 2 \cdot 5 \cdot 3 x i + (3 x i)^{2}

5^{2} = 25

- 2 \cdot 5 \cdot 3 x i = - 30 x i

(3 x i)^{2} = - 9 x^{2}

= 25 - 30 x i - 9 x^{2}

Rewrite in standard complex form:

(25 - 9 x^{2}) - 30 x i

= (25 - 9 x^{2}) - 30 x i

- \frac{300 ( - 3 x ^{2} - 25 )}{( x ^{2} - 25 ) ^{3}}

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

(x - 25) (x + 25)

(x - x - 2) (x + x - 2)

β (x, y + 1)