Question

Descompuneți în factori. 32a²b²-8(a+b)​²​

Answer 1

   

$\displaystyle\bf\\Descompunem~in~factori:~~~~~32a^2b^2-8(a+b)^2\\\\Folosim~formula:~~~~a^2-b^2=(a+b)(a-b)\\\\Rezolvare:\\\\32a^2b^2-8(a+b)^2=\\\\=2\Big[16a^2b^2-4(a+b)^2\Big]=\\\\=2\left[\Big(4ab\Big)^2-\Big(2(a+b)\Big)^2\right]=\\\\=2\Big(4ab+2(a+b)\Big)\Big(4ab-2(a+b)\Big)=\\\\=\boxed{\bf2(4ab+2a+2b)(4ab-2a-2b)}$