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

The solution to (1+2sqrt(x-2))^2 is 4x+4sqrt(x-2)-7

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

simplify

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

4 x + 4 x - 2 - 7

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

1^{2} + 2 \cdot 1 \cdot 2 x - 2 + (2 x - 2)^{2} : 4 x + 4 x - 2 - 7

= 4 x + 4 x - 2 - 7

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

(\frac{k ( k + 1 )}{2})^{2}

(2 sin (x) + 1) (2 sin (x) - 1)

(e^{t} + t e^{t})^{2}

(e^{- x} - 2)^{2}