Factorisation help

[F.AAAA]

Hi,
I need help understanding how 1/4k^2(k + 1)^2 + (k + 1)^3 can factorise to become 1/4(k + 1)^2(k^2 + 4k + 4). Any help would be greatly appreciated.

 

[Otis]

Please read and follow the forum guidelines, F.AAAA.

Start by factoring out the common factor: (k+1)^2.

If it helps you to see how, you can always make a temporary substitution first.

Let z = k+1

Then you have:

1/4 * k^2 * z^2 + z^3

After you factor out the common factor z^2, back-substitute k+1 for z in your result. Then show us what you got.

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The next step will involve a factorization like these examples:

1/2*t + t + 1 = 1/2(t + 2t + 2)

1/3*t + t + 1 = 1/3(t + 3t + 3)

?

 

[F.AAAA]

Please read and follow the forum guidelines, F.AAAA.

Start by factoring out the common factor: (k+1)^2.

If it helps you to see how, you can always make a temporary substitution first.

Let z = k+1

Then you have:

1/4 * k^2 * z^2 + z^3

After you factor out the common factor z^2, back-substitute k+1 for z in your result. Then show us what you got.

---

The next step will involve a factorization like these examples:

1/2*t + t + 1 = 1/2(t + 2t + 2)

1/3*t + t + 1 = 1/3(t + 3t + 3)

?

Thank you very much it suddenly clicked for me after I factored out the (k+1)