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The factors of a2 - b2 - 4c2 + 4d2 - 4(ad - bc) are :

(a) (a + 2d + b + 2c)(a - 2d - b + 2c) 

(b) (a - 2d + b - 2c)(a + 2d - b + 2c) 

(c) (a - 2d + b - 2c)(a - 2d - b + 2c) 

(d) (a - 2d - b - 2c)(a + 2d - b + 2c) 

1 Answer

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Best answer

(c) (a - 2d + b - 2c)(a - 2d - b + 2c)

a2 - b2 - 4c2 + 4d2 - 4(ad - bc)

= a2 - b2 - 4c2 + 4d2 - 4ad + 4bc

= (a2 - 4ad + 4d2) - (b2 - 4bc + 4c2)

= (a - 2d)2 - (b - 2c)2

= (a - 2d + b - 2c)(a - 2d - b + 2c)

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