Question

Urgent i've tried numerous times but i've been unable to factor it

Answer 1

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

Explanation:

4c² - a² - 6ab - 9b²

= 4c² - (a² + 6ab + 9b²) ← the terms in the parenthesiis are a perfect square )

= 4c² - (a + 3b)² ← this is a difference of squares which factors in general as

a² - b² = (a - b)(a + b) , then

= (2c)² - (a + 3b)²

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

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

Answer 2

`(2c+a+3b)(2c-a-3b)`

Explanation:

Given expression:
`4c^2-a^2-6ab-9b^2`

Factor
`-a^2-6ab-9b^2`

`\implies -(a^2+6ab+9b^2)`

`\implies -(a+3b)(a+3b)`

`\implies -(a+3b)^2`

Factor
`4c^2`

`\implies(2c)(2c)`

`\implies (2c)^2`

Therefore,

`(2c)^2-(a+3b)^2`

Difference of Two Squares:
`x^2-y^2=(x+y)(x-y)`

`x^2=(2c)^2\implies x=2c`

`y^2=(a+3b)^2 \implies y=a+3b`

Therefore,

`\implies (2c + a + 3b)(2c - (a + 3b))`

`\implies (2c+a+3b)(2c-a-3b)`