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

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

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

factor

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

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

Solution steps

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

Simplify

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

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

Apply Difference of Two Squares Formula:

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

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

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

Apply rule:

(a) = a

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

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

\frac{( 2 x ) ^{2}}{( 5 y ) ^{4}}

7 (x - 1) = 5 (x - 3)

∣ 3 x + 10 ∣ = 10

\frac{6}{4 - 13 i}

\frac{2 π}{1.1}

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