What is (2x+sqrt(4x^2-1))^2 ?

The solution to (2x+sqrt(4x^2-1))^2 is 8x^2+4xsqrt(4x^2-1)-1

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simplify (2x+sqrt(4x^2-1))^2

simplify

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

8 x^{2} + 4 x 4 x^{2} - 1 - 1

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(2 x)^{2} + 2 \cdot 2 x 4 x^{2} - 1 + (4 x^{2} - 1)^{2} : 8 x^{2} + 4 x 4 x^{2} - 1 - 1

= 8 x^{2} + 4 x 4 x^{2} - 1 - 1

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

(\frac{c}{2} - \frac{d}{3}) d^{2}

(5 - x 5)^{2}

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

\frac{( x - 3 ) ^{2}}{4 ( x - 1 )}

What is (2x+sqrt(4x^2-1))^2 ?
The solution to (2x+sqrt(4x^2-1))^2 is 8x^2+4xsqrt(4x^2-1)-1