Factor out completely: 4a^2c^2 - (a^2-b^2 c^2) ^2

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Mathematics

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3 March, 15:25

Factor out completely: 4a^2c^2 - (a^2-b^2 c^2) ^2

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Abby Proctor · Answer 1

The expression 4a^2c^2 - (a^2-b^2+c^2) ^2 has to be factored.

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

=> (2ac) ^2 - (a^2 - b^2 + c^2) ^2

=> (2ac - a^2 + b^2 - c^2) (2ac + a^2 - b^2 + c^2)

=> (b^2 - (a^2 - 2ac + c^2)) ((a^2 + 2ac + c^2) - b^2)

=> (b^2 - (a - c) ^2) ((a + c) ^2 - b^2)

=> (b - a + c) (b + a - c) (a + b + c) (a - b + c)

The factorized form of 4a^2c^2 - (a^2-b^2+c^2) ^2 is (b - a + c) (b + a - c) (a + b + c) (a - b + c)