Question

lets see who answers the most and the best q1 factorise 4a^2-(4b^2+4bc+c^2) q2 factorise 9a^2+3a-8b-64b^2 q3 factorise 4a^2-12a+9-49b^2​

Answer 1

1.

$4 {a}^{2} - (4 {b}^{2} + 4bc + {c}^{2} ) \\ = 4 {a}^{2} - (( {2b})^{2} + 2(2b)(c) + ({c})^{2} ) \\ = ({2a})^{2} - (2b + c)^{2}$

Using,

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

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

2.

$9 {a}^{2} + 3a - 8b - 64 {b}^{2} \\ = 9 {a}^{2} - 64 {b}^{2} + 3a - 8b \\ = {(3a)}^{2} - {(8b)}^{2} + 3a - 8b \\ = (3a + 8b)(3a - 8b) + 1(3a - 8b) \\ = (3a - 8b)(3a + 8b + 1)$

3.

$4 {a}^{2} - 12a + 9 - 49 {b}^{2} \\ = (2a) ^{2} - 2(2a)(3) + {3}^{2} - {(7b)}^{2} \\ = (2a - 3)^{2} - {(7b)}^{2} \\ = (2a - 3 + 7b)(2a - 3 - 7b)$

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