Question

Considera estas dos operaciones: $\begin{align*} a\,\blacklozenge\,b &= a^2 - b^2 \\ a \star b &= (a - b)^2 \end{align*}$

Calcula el valor:

$(5\,\blacklozenge\,3) \star 6$

Consider these two operations: $\begin{align*} a\,\blacklozenge\,b &= a^2 - b^2 \\ a \star b &= (a - b)^2 \end{align*}$

Compute the value:

$(5\,\blacklozenge\,3) \star 6$

$-20$

$4$

$16$

$100$

$220$

Usando las definiciones, $\begin{align*} (5\,\blacklozenge\,3) \star 6 &= (5^2-3^2) \star 6 \\ &=16 \star 6 \\ &=(16-6)^2\\ &= 100\end{align*}$

Por lo tanto, la respuesta correcta es D.

Using the definitions, $\begin{align*} (5\,\blacklozenge\,3) \star 6 &= (5^2-3^2) \star 6 \\ &=16 \star 6 \\ &=(16-6)^2\\ &= 100\end{align*}$

Thus, the correct answer is D.