Question

Descompuneți în factori. 4(x-2)²+20(x-2)+25-(x+1)²​

Answer 1

 

$\displaystyle\bf\\Descompunem~in~factori:~~~~4(x-2)^2+20(x-2)+25-(x+1)^2\\\\Folosim~formulele:\\\\a^2+2ab+b^2=(a+b)^2\\a^2-b^2=(a+b)(a-b)$

.

$\displaystyle\bf\\Rezolvare:\\\\4(x-2)^2+20(x-2)+25-(x+1)^2=\\\\=\Big(4(x-2)^2+20(x-2)+25\Big)-\Big(x+1\Big)^2=\\\\=\left[\Big(2(x-2)\Big)^2+2\times2(x-2)\times5+5^2\right]-\Big(x+1\Big)^2=\\\\=\Big(2(x-2)+5\Big)^2-\Big(x+1\Big)^2=\\\\=\Big(2x-4+5\Big)^2-\Big(x+1\Big)^2=\\\\=\Big(2x+1\Big)^2-\Big(x+1\Big)^2=\\\\=\Big[(2x+1)+(x+1)\Big]\Big[(2x+1)-(x+1)\Big]=\\\\=(2x+1+x+1)(2x+1-x-1)=\\\\=(3x+2)(x)=\\\\=\boxed{\bf x(3x+2)}$