simplify (2x+i)^2

Solution

simplify

(2 x + i)^{2}

(4 x^{2} - 1) + 4 x i

Solution steps

(2 x + i)^{2}

Apply Perfect Square Formula:

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

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

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

(2 x)^{2} = 4 x^{2}

2 \cdot 2 x i = 4 x i

i^{2} = - 1

= 4 x^{2} + 4 x i - 1

Rewrite in standard complex form:

(4 x^{2} - 1) + 4 x i

= (4 x^{2} - 1) + 4 x i

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

\frac{s ^{2} + 6 s + 9}{( s - 1 ) ( s - 2 ) ( s + 4 )}

(x + 23) (x - 23)

(1 + 5 x i)^{2}

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