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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(1 + sin (t))^{2}

t (x) x^{^{''}} + (2 t (x) - 4) x^{^{'}} + 2 x

s + i (- s^{2} + 1)

\frac{s ^{2} + 20 s + 150}{( s + 2.93 ) ( s + 17.07 )}

\frac{4 ( s + 1 )}{( s ^{2} + 2 s + 5 ) ^{2}}

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