Question

factorise 25a²-9b²+12 bc-4c²​

Answer 1

Step-by-step explanation:

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Answer 2

The factorisation of $25a^2-9b^2+12 bc-4c^2$ is equal to "(5a + 3b - 2c)(5a - 3b + 2c)".

Step-by-step explanation:

We have,

$25a^2-9b^2+12 bc-4c^2$

To find, the factorisation of $25a^2-9b^2+12 bc-4c^2$ = ?

∴ $25a^2-9b^2+12 bc-4c^2$

$=25a^2-(9b^2-12 bc+4c^2)$

$=25a^2-((3b)^2-2(3b)(2c)+(2c)^2)$

Using the algebraic identity,

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

$=25a^2-(3b-2c)^2$

$=(5a)^2-(3b-2c)^2$

Using the algebraic identity,

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

= (5a + 3b - 2c)(5a - (3b - 2c))

= (5a + 3b - 2c)(5a - 3b + 2c)

Thus, the factorisation of $25a^2-9b^2+12 bc-4c^2$ is equal to "(5a + 3b - 2c)(5a - 3b + 2c)".