please help and explain?

Question

factor this equation and EXPLAIN every step please!!! if u answer thank u so much i really need help:

3x^2(x+2)^2 + 2x^3(x+2)

Answer 1

This is not an equation, it's an expression. Both terms contain the factors x² and (x + 2)
So we can put these outside of a pair of brackets.
So first step is to write:
x²(x + 2)( + )
Now we have to decide what to put inside the second pair of brackets. To get the first term we have to multiply
x²(x + 2) by 3(x + 2), so 3(x + 2) goes inside the brackets
To get the second term we multiply x²(x + 2) by 2x, so 2x goes inside the brackets.
Our expression now becomes:
x²(x + 2){3(x + 2) + 2x}

Finally we multiply out the inner brackets so that
3(x + 2) becomes 3x + 6, and then collect together like terms to finish with the solution:

3x²(x + 2)² + 2x³(x + 2)
= x²(x + 2){3(x + 2) + 2x}
= x²(x + 2)(3x + 6 + 2x)
= x²(x + 2)(5x + 6)

Answer 2

Hm.. you already have two answers but no explanations.

I would start by multiplying everything through.
First, (x+2)^2 is x^2 + 4x + 4.

So you have:

3x^2 (x^2 + 4x + 4 ) + 2x^3 ( x+2)

Now just distribute the coefficients (the numbers in front of the parentheses).

3x^4 + 12x^3 + 12x^2 + 2x^4 + 4x^3

Combine like terms.

5x^4 + 16x^3 + 12x^2

Nice answer, but you're still not done.

Factor out an x^2

x^2(5x^2 + 16x + 12)

Factor the quadratic using the quadratic formula or your brain.

Your final answer would be

(x^2)(5x + 6)*(x + 2)

My guess is that this equation was oringinally set to zero in which case you would have to set each factor to zero to get your x values.

x^2 = 0 5x+6 = 0 x+2 = 0
x = 0 x = -6/5 x = -2

If you did the quadratic formula, you would have gotten -6/5 and -2 but don't forget about that x^2 out in front. Hope this helped.

Answer 3

This polynom may be written like this:
(x+2)(3x^2(x+2)+2x^3)=
(x+2)x^2(3(x+2)+2x)=
x^2(x+2)(5x+6)=
x^2(x+2)(x+6/5)

Satisfied?

Answer 4

(x+2)^2 = x^2 + 4x + 4

3x^2(x^2+4x+4) + 2x^4 + 4x^3
3x^4 +12x^3 + 12 x^2 + 2x^4 + 4x^3
5x^4 + 16x^3 + 12x^2

Answer 5

x^2(5x^2 + 16x^4+ 12)