please solve Recall that b3 a3 baa2 ab b62 Let fx x3 Th

please solve

Recall that b^3 - a^3 = (b-a)(a^2 + ab + b62), Let f(x) = x^3. The fraction f(x)-f(2)/x-2 simplifies to x^2 + 2x + 4. f. F(x-2)/x-2. x^2 - 2x + 4.

Solution

given f(x)=x³

[f(x)-f(2)]/(x-2)

=[x³-2³]/(x-2)

=[(x-2)(x²+x2+2²)]/(x-2)

=[(x-2)(x²+2x+4)]/(x-2)

cancel out x-2 in numerator and denominator

=x²+2x+4