Answer: (a) 8(x + a) --> 8x + 8a
(b) 8(2x + h) --> 16x + 8h
Step-by-step explanation:
f(x) = 8x²
f(a) = 8a²
[tex]\dfrac{f(x)-f(a)}{x-a}\quad = \quad \dfrac{8x^2-8a^2}{x-a}\quad = \quad \dfrac{8(x-a)(x+a)}{x-a}=\large\boxed{8(x+a)}[/tex]
f(x + h) = 8(x + h)²
= 8(x² + 2xh + h²)
= 8x² + 16xh + 8h²
f(x) = 8x²
[tex]\dfrac{f(x+h)-f(x)}{h} = \dfrac{(8x^2+16xh+8h^2)-8x^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{16xh + 8h^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{8h(2x + h)}{h}\\\\\\.\qquad \qquad \qquad \quad =\large\boxed{8(2x+h)}[/tex]
