Question

Factorise:
4a^2-9b^2-16c^2+24bc

Answer 1

this is the answer for your question.

Answer 2

Answer:

The factorized form is $(2a+3b-4c)(2a-3b+4c$

Step-by-step explanation:

The expression which we need to factorized is

$4a^2-9b^2-16c^2+24bc$

Let us write the last three terms as

$4a^2-(9b^2+16c^2-24bc)\\\\=4a^2-((3b)^2+(4c)^2-2\cdot3b\cdot4c)$

Now, using the formula $a^2+b^2-2ab=(a-b)^2$

$4a^2-(3b-4c)^2$

Write in perfect squares form

$(2a)^2-(3b-4c)^2$

Using the difference of squares formula $a^2-b^2=(a+b)(a-b)$

$(2a+3b-4c)(2a-3b+4c$