Cho: $\left( I \right):4{{x}^{2}}+4x-9{{y}^{2}}+1=\left( 2x+1+3y \righ

Cho:

$\left( I \right):4{{x}^{2}}+4x-9{{y}^{2}}+1=\left( 2x+1+3y \right)\left( 2x+1-3y \right)$

$\left( II \right):5{{x}^{2}}-10xy+5{{y}^{2}}-20{{z}^{2}}=5\left( x+y+2z \right)\left( x+y-2z \right)$

• A.

  $\Large \left( I \right)$ đúng, $\Large \left( II \right)$ sai.

• B.

  $\Large \left( I \right)$ sai, $\Large \left( II \right)$ sai.

• C.

  $\Large \left( I \right)$, $\Large \left( II \right)$ đều sai.

• D.

  $\Large \left( I \right)$, $\Large \left( II \right)$ đều đúng.

Ta có:

 $\Large \begin{align}  & 4{{x}^{2}}+4x-9{{y}^{2}}+1 \\  & =\left( 4{{x}^{2}}+4x+1 \right)-9{{y}^{2}} \\  & ={{\left( 2x+1 \right)}^{2}}-{{\left( 3y \right)}^{2}} \\  & =\left( 2x+1+3y \right)\left( 2x+1-3y \right) \\ \end{align}$

Nên $\Large \left( I \right)$ đúng.

$\Large \begin{align}  & 5{{x}^{2}}-10xy+5{{y}^{2}}-20{{z}^{2}} \\  & =5\left( {{x}^{2}}-2xy+{{y}^{2}}-4{{z}^{2}} \right) \\  & =5\left[ {{\left( x-y \right)}^{2}}-{{\left( 2z \right)}^{2}} \right] \\  & =5\left( x-y-2z \right)\left( x-y+2z \right) \\ \end{align}$

Nên $\Large \left( II \right)$ sai.