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

The solution to (2-sqrt(3x+2))^2 is 3x-4sqrt(3x+2)+6

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

simplify

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

3 x - 4 3 x + 2 + 6

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

2^{2} - 2 \cdot 2 3 x + 2 + (3 x + 2)^{2} : 3 x - 4 3 x + 2 + 6

= 3 x - 4 3 x + 2 + 6

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

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

\frac{10 ( x - 4 )}{3}

\frac{10 x - 6}{( x - 3 ) ^{4}}

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