What is (-sqrt(9-r^2)+3)^2 ?

The solution to (-sqrt(9-r^2)+3)^2 is -r^2-6sqrt(9-r^2)+18

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simplify (-sqrt(9-r^2)+3)^2

simplify

(- 9 - r^{2} + 3)^{2}

- r^{2} - 6 9 - r^{2} + 18

Solution steps

(- 9 - r^{2} + 3)^{2}

Apply Perfect Square Formula:

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

(- 9 - r^{2} + 3)^{2} = (- 9 - r^{2})^{2} + 2 (- 9 - r^{2}) \cdot 3 + 3^{2}

= (- 9 - r^{2})^{2} + 2 (- 9 - r^{2}) \cdot 3 + 3^{2}

Simplify

(- 9 - r^{2})^{2} + 2 (- 9 - r^{2}) \cdot 3 + 3^{2} : - r^{2} - 6 9 - r^{2} + 18

= - r^{2} - 6 9 - r^{2} + 18

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\frac{t ^{3} + 2 t ^{2} + 3 t + 2}{( t ^{2} + 1 ) ^{2}}

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What is (-sqrt(9-r^2)+3)^2 ?
The solution to (-sqrt(9-r^2)+3)^2 is -r^2-6sqrt(9-r^2)+18