What is (sqrt(x-3)+1)^2 ?

The solution to (sqrt(x-3)+1)^2 is x+2sqrt(x-3)-2

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simplify (sqrt(x-3)+1)^2

simplify

(x - 3 + 1)^{2}

x + 2 x - 3 - 2

Solution steps

(x - 3 + 1)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x + 2 x - 3 - 2

\frac{( 4 x + 9 ) ^{\frac{3}{2}} - 27}{6}

(cos (t) - 4 sin (t))^{2}

\frac{36 x}{( 9 - x ^{2} ) ^{2}}

(- b + b^{2} + 4 a c)^{2}

\frac{1}{( 2 x )} 5