Question

Descompuneti in factori:
$(4x+1)^{2}-(2x+3)^{2}$
cu explicatie

Answer 1

$=(16x^2+8x+1^2)-(4x^2+12x+3^2)=16x^2+8x+1-4x^2-12x-$
$-9=12x^2-4x-8=12x^2+12x-8x-8=(12x^2+12x)-(8x+8)$
$=12x(x+1)-8(x+1)=(12x-8)(x+1)=4(3x-2)(x+1)$

Answer 2

 $Mai \;comod\;este\;utilizarea\; formulei\;\; a^2-b^2=(a+b)(a-b) \;!\\ a^2=(4x+1)^2 \;\;deci\;a=4x+1\;\;;\;\;b^2=1^2\;\;deci\;\;b=1\;...\\ \Rightarrow\;\;(4x+1)^2-(2x+3)^2=(4x+1 + 2x+3)(4x+1 -2x-3)=\\ =2*(3x+2)*2(x-1)=4*(3x+2}*(x-1)\;$