\begin{gathered}8a^2+16ab+8b^2-4a^2+4b^2=8(a^2+2ab+b^2)-4(a^2-b^2)==8(a+b)^2-4(a+b)(a-b)==(a+b)(8(a+b)-4(a-b))=(a+b)(8a+8b-4a+4b)==(a+b)(4a+12b)=4(a+b)(a+3b)\end{gathered}
8a
2
+16ab+8b
2
−4a
2
+4b
2
=8(a
2
+2ab+b
2
)−4(a
2
−b
2
)=
=8(a+b)
2
−4(a+b)(a−b)=
=(a+b)(8(a+b)−4(a−b))=(a+b)(8a+8b−4a+4b)=
=(a+b)(4a+12b)=4(a+b)(a+3b)
