Question

divide 20a(squared) - 11 by 4a +2

Answer 1

$(20a^2-11):(4a+2)=(20a^2-11):[2(2a+1)]\\\\=\frac{5\cdot4a^2-5+5-11}{2(2a+1)}=\frac{5(4a^2-1)-6}{2(2a+1)}=\frac{5[(2a)^2-1^2]-6}{2(2a+1)}\\\\=\frac{5(2a-1)(2a+1)-6}{2(2a+1)}=\frac{5(2a-1)(2a+1)}{2(2a+1)}-\frac{6}{2(2a+1)}=\frac{5}{2}(2a-1)-\frac{6}{4a+2}\\-----------------------------\\20a^2-11=(4a+2)\cdot\frac{5}{2}(2a-1)-6=2(2a+1)\cdot\frac{5}{2}(2a-1)-6\\\\=5(2a+1)(2a-1)-6$