What is (2a-sqrt((x-c)^2+y^2))^2 ?

The solution to (2a-sqrt((x-c)^2+y^2))^2 is 4a^2-4asqrt((x-c)^2+y^2)+(x-c)^2+y^2

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simplify (2a-sqrt((x-c)^2+y^2))^2

simplify

(2 a - (x - c)^{2} + y^{2})^{2}

4 a^{2} - 4 a (x - c)^{2} + y^{2} + (x - c)^{2} + y^{2}

Solution steps

(2 a - (x - c)^{2} + y^{2})^{2}

Apply Perfect Square Formula:

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

(2 a - (x - c)^{2} + y^{2})^{2} = (2 a)^{2} - 2 \cdot 2 a (x - c)^{2} + y^{2} + ((x - c)^{2} + y^{2})^{2}

= (2 a)^{2} - 2 \cdot 2 a (x - c)^{2} + y^{2} + ((x - c)^{2} + y^{2})^{2}

(2 a)^{2} = 4 a^{2}

- 2 \cdot 2 a (x - c)^{2} + y^{2} = - 4 a (x - c)^{2} + y^{2}

((x - c)^{2} + y^{2})^{2} = (x - c)^{2} + y^{2}

= 4 a^{2} - 4 a (x - c)^{2} + y^{2} + (x - c)^{2} + y^{2}

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What is (2a-sqrt((x-c)^2+y^2))^2 ?
The solution to (2a-sqrt((x-c)^2+y^2))^2 is 4a^2-4asqrt((x-c)^2+y^2)+(x-c)^2+y^2