Answer:
(2a + 3b)(2a - b)
Explanation:
4a² + 4ab - 3b²
consider the factors of the product of the coefficient of a² and b² which sum to give the coefficient of the ab- term.
product = 4 × - 3 = - 12 and sum = 4
the factors are + 6 and - 2
use these factors to split the ab- term
= 4a² + 6ab - 2ab - 3b² ( factor the first/second and third/fourth terms )
= 2a(2a + 3b) - b(2a + 3b) ← factor out (2a + 3b) from each term
= (2a + 3b)(2a - b)