Question

a²+4b²-4ab-4c² factorise

Answer 1

a² + 4b² - 4ab - 4c²

=> a² + (2b)² - 2×a×(2b) - (2c)²

use identity

(a-b)² = a²+b²-2ab

now

=> (a — 2b)² — (2c)²

use identity

a² — b² = (a+b)(a-b)

=> (a — 2b +2c) ( a— 2b — 2c)

is the factor.

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Answer 2

${a}^{2} + {4b}^{2} - 4ab - 4 {c}^{2} \\{ {a}^{2} + {(2b)}^{2} - 2 \times a \times 2b \: } \: \: - {(2c)}^{2} \\ using \: dentity \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ {a}^{2} + {(2b)}^{2} - 2 \times a \times 2b \:= {(a - 2b)}^{2} \\ {(a - 2b)}^{2} - {(2c)}^{2} = \\ using \: dentity \: {a }^{2} - {b}^{2} = \\ (a + b)(a - b) \\ answer \: is \:( a - 2b + c)(a - 2c - c)$

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