which expression has the greatest value when $x = 3$? $2x^{3}$ $2x^{3}+5$ $(2x)^{3}$ $(x - 1)^{3}$

Answer:

$(2x)^{3}$

Explanation:

Step1: Calculate value of $2x^{3}$ when $x = 3$

$2\times3^{3}=2\times27 = 54$

Step2: Calculate value of $2x^{3}+5$ when $x = 3$

$2\times3^{3}+5=54 + 5=59$

Step3: Calculate value of $(2x)^{3}$ when $x = 3$

$(2\times3)^{3}=6^{3}=216$

Step4: Calculate value of $(x - 1)^{3}$ when $x = 3$

$(3 - 1)^{3}=2^{3}=8$

Step5: Compare the values

$8<54<59<216$, so $(2x)^{3}$ has the greatest value.