What is factor 4a^2c^2-(c^2-b^2+a^2)^2 ?

The solution to factor 4a^2c^2-(c^2-b^2+a^2)^2 is (2ac+c^2-b^2+a^2)(2ac-c^2+b^2-a^2)

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factor 4a^2c^2-(c^2-b^2+a^2)^2

factor

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

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

Solution steps

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

Simplify

4 a^{2} c^{2} : (2 a c)^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Simplify

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

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

3 + \frac{1}{8}

5 i x^{2} + 11 x - 2 i

- 4 < 2 x - 2 \leq 6

x^{2} + 10 x = - 7

What is factor 4a^2c^2-(c^2-b^2+a^2)^2 ?
The solution to factor 4a^2c^2-(c^2-b^2+a^2)^2 is (2ac+c^2-b^2+a^2)(2ac-c^2+b^2-a^2)