What is (sqrt(2x-\sqrt{4x-3)})^4 ?

The solution to (sqrt(2x-\sqrt{4x-3)})^4 is 4x^2-4xsqrt(4x-3)+4x-3

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simplify (sqrt(2x-\sqrt{4x-3)})^4

simplify

(2 x - 4 x - 3)^{4}

4 x^{2} - 4 x 4 x - 3 + 4 x - 3

Solution steps

(2 x - 4 x - 3)^{4}

Rewrite

4

2 \cdot 2

= (2 x - 4 x - 3)^{2 \cdot 2}

Apply exponent rule:

a^{b c} = (a^{b})^{c},

assuming

a \geq 0

(2 x - 4 x - 3)^{2 \cdot 2} = ((2 x - 4 x - 3)^{2})^{2}

= ((2 x - 4 x - 3)^{2})^{2}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(2 x - 4 x - 3)^{2} = 2 x - 4 x - 3

= (2 x - 4 x - 3)^{2}

Apply Perfect Square Formula:

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

(2 x - 4 x - 3)^{2} = (2 x)^{2} - 2 \cdot 2 x 4 x - 3 + (4 x - 3)^{2}

= (2 x)^{2} - 2 \cdot 2 x 4 x - 3 + (4 x - 3)^{2}

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

- 2 \cdot 2 x 4 x - 3 = - 4 x 4 x - 3

(4 x - 3)^{2} = 4 x - 3

= 4 x^{2} - 4 x 4 x - 3 + 4 x - 3

(\frac{144}{36})^{2}

15 d^{15} e^{15} f^{2} \cdot 5 d^{5} e^{5} f

- y^{2}

\frac{2 \cdot 400 \cdot 300 \cdot 500}{5 \cdot 400 \cdot ( 1 - \frac{400}{1} )}

(x - 7)^{2} (y + 3)^{2}

What is (sqrt(2x-\sqrt{4x-3)})^4 ?
The solution to (sqrt(2x-\sqrt{4x-3)})^4 is 4x^2-4xsqrt(4x-3)+4x-3