Question

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

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

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

Step-by-step explanation:

The expression which we need to factorise 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)