Question

Evaluate the expressions \(3 x^{2}\) and \((3 x)^{2}\) when \(x=4\)

Short answer

The expression \(3 x^{2}\) evaluates to 48 and the expression \((3 x)^{2}\) evaluates to 144 when \(x=4\).

Step-by-step solution

Substitute x in \(3 x^{2}\)

First, we need to evaluate the expression \(3 x^{2}\). We substitute \(x=4\) into the expression, which gives us \(3 * 4^{2}\).

Simplify expression \(3 x^{2}\)

Now we need to do the calculation. Following correct order of operations, we first calculate the exponent, \(4^{2} = 16\). Thus, the expression becomes \(3 * 16\). We then perform the multiplication, which gives us a result of 48.

Substitute x in \((3 x)^{2}\)

Next, we substitute \(x=4\) into the expression \((3 x)^{2}\) which gives us \((3 * 4)^{2}\).

Simplify expression \((3 x)^{2}\)

Now we need to do the calculation. This time, since the parentheses change the order of operations, we first perform the multiplication inside the parentheses: \(3 * 4 = 12\). Thus, the expression becomes \(12^{2}\). We then perform the exponentiation, which gives us a result of 144.