Answer:
- [tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]
==========================
Identities we will use:
- [tex]a^2+2ab+b^2=(a+b)^2[/tex]
- [tex]a^2-b^2=(a+b)(a-b)[/tex]
===========================
Given expression:
Factorize it by completing the square and setting the difference of squares:
- [tex]4a^2+4a + 1-6=[/tex]
- [tex](2a)^2+2*1*2a + 1^2-6=[/tex]
- [tex](2a+1)^2-6=[/tex]
- [tex](2a + 1+\sqrt{6})(2a + 1-\sqrt{6})[/tex]
