Questions: f(h) = (16(2+h)^2 - 64)/h

Solution Steps

To solve the given function \( f(h) = \frac{16(2+h)^{2} - 64}{h} \), we need to simplify the expression. The approach involves expanding the squared term, simplifying the numerator, and then dividing by \( h \).

First, we expand the squared term in the numerator of the function \( f(h) = \frac{16(2+h)^{2} - 64}{h} \). The expression \( (2+h)^{2} \) expands to \( 4 + 4h + h^{2} \).

Substitute the expanded form into the numerator: \[ 16(4 + 4h + h^{2}) - 64 \] This simplifies to: \[ 64 + 64h + 16h^{2} - 64 \] Further simplification gives: \[ 16h^{2} + 64h \]

Now, divide the simplified numerator by \( h \): \[ \frac{16h^{2} + 64h}{h} = 16h + 64 \]

Final Answer