putnam821
Answered

The last term in the expansion of the binomial (3x+6)^3 is?

Verified Answer :

The last term will be the second part cubed or 6^3 which equals 216

charlottekrist
  1. Use Cube of sum : (a+b)^3 = a^3+3a^2b+3ab^2+b^3
    (3x+6)((3x)^2+23x6+6^2)

    2. Use multiplication distributive property (xy)^a=x^ay^a
    (3x+6)(3^2x^2+23x+6+6^2)

    3. Simplify 3^2 to 9
    (3x+6)(9X^2+2    3X6+6^2)

    4. Simplify 6^2 to 36
    (3x+6)(9x^2+2    3x6+36)

    5. Simplify 2    3x*6 to 36x
    (3x+6)(9x^2+36x+36)

    6. Distribute sum groups
    3x(9x^2+36x+36)+6(9x^2+36x+36)

    7. Distribute
    27x^3+108x^2+108x+6(9x^2+36x+36)

    8. Distribute 
    27x^3+108x^2+108x+54x^2+216x+216

    9. Collect like terms
    27x^3+(108x^2+54x^2)+(108x+216x)+216

    10. Simplify 
    27x^3+162x^2+324x+216

    The last term is therefore, 216. Have a nice day :D

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