CUBICS MATH PROBLEM - How do I expand this cubic form?

Question

The questions on the book says:

3. From the cubic form, give your answer in factor form and in expanded form

My cubic function/form is: 2(x+1)² (x-3)

1ST STEP: (solve the square, by re-writing the bracket) 2(x+1) (x+1) (x-3)

2ND STEP: (ignore the first bracket and work with the other two) (x+1) (x-3)

3RD STEP: (expand both brackets) x²-3x+x-3

4TH STEP: (then bring back the bracket which was ignored) 2(x+1) x²-3x+x-3

HERE COMES MY QUESTION. what do I do now? Before I was suppose to multiply what I expanded with the "ignored bracket" but there is a 2 in the middle of the way, what to do I do???

THE CORRECT ANSWER: 2x³-2x²-10x-6

Answer 1

The direct answer is: leave the 2 until the end. Use the distributive law to multiply the trinomial by the binomial, then multiply by 2.

However, you did this the hard way: you should start with the square first

2(x² + 2x + 1)(x-3) now use the distributive law and finally multiply by 2.

You should remember that the square of a binomial is: the square the first + twice the first times the second + the square of the second.

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