Precalculus, Chapter 9, 9.5, Section 9.5, Problem 39

Let's use the binomial formula, (x+y)^n=sum_(k=0)^n ((n),(k))(x)^(n-k)*y^k to expand 2(x-3)^4+5(x-3)^2
2(x-3)^4=2(((4),(0)).x^(4-0)*(-3)^0+((4),(1))*x^(4-1)*(-3)^1+((4),(2))*x^(4-2)*(-3)^2+((4),(3))*x^(4-3)*(-3)^3+((4),(4))*x^(4-4)*(-3)^4)
=2(x^4+(4!)/(1!(4-1)!)*x^3*(-3)+(4!)/(2!(4-2)!)*x^2*(-3)^2+(4!)/(3!(4-3)!)*x^1*(-3)^3+(-3)^4)
=2(x^4+(4*3!)/(3!)*x^3*(-3)+(4*3*2!)/(2!2!)*x^2*(-3)^2+(4*3!)/(3!1!)*x*(-3)^3+(-3)^4)
=2(x^4-12x^3+54x^2-108x+81)
5(x-3)^2=5(((2),(0))*x^(2-0)*(-3)^0+((2),(1))*x^(2-1)*(-3)^1+((2),(2))*x^(2-2)*(-3)^2)
=5(x^2+(2!)/(1!(2-1)!)*x^1*(-3)^1+(-3)^2)
=5(x^2-6x+9)
:.2(x-3)^4+5(x-3)^2=2(x^4-12x^3+54x^2-108x+81)+5(x^2-6x+9)
=2x^4-24x^3+108x^2-216x+162+5x^2-30x+45
Now combine the like terms,
=2x^4-24x^3+108x^2+5x^2-216x-30x+162+45
=2x^4-24x^3+113x^2-246x+207