Question

Find and simplify the expression if f(x)=x2 - 2.f(8 + h)f(8 + h) =(Simplify your answer. Do not factor.)

Answer 1

`\text{Answer : h}^2\text{ + 16h + 62}`

Given that: f(x) = x^2 - 2

find f(8 + h)

The implies that, substitute the value of x = 8 + h

`\begin{gathered} \text{ Since, f(x) = x}^2\text{ - 2} \\ f(8+h)=(8+h)^2\text{ - 2} \\ \text{Expand the bracket} \\ f(8+\text{ h) = (8 + h)(8 + h) - 2} \\ f(8\text{ + h) = 8 }\cdot8\text{ + 8}\cdot h\text{ + 8}\cdot h+h^2\text{ - 2} \\ f(8+h)=64+8h+8h+h^2\text{ - 2} \\ f(8+h)=64+16h+h^2\text{ - 2} \\ f(8+h)=h^2\text{ + 16h + 64 - 2} \\ f(8+h)=h^2\text{ + 16h + 62} \\ \end{gathered}`
`\text{Therefore, the answer is h}^2\text{ + 16h + 62}`