Simplifying $3x^2(x+8)^3+3x^3(x+8)^2$












0














I found the derivative of $[x^3(x+8)^3]$ to equal $3x^2(x+8)^3+3x^3(x+8)^2$ using Chain Rule.



Somehow it can simplify further to: $6x^2(x+4)(x+8)^2$.



I can't manage the steps to get it to the simplified form.






calculus derivatives exponential-function







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  • 3




    Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
    – TheSimpliFire
    Nov 29 at 19:33
















0














I found the derivative of $[x^3(x+8)^3]$ to equal $3x^2(x+8)^3+3x^3(x+8)^2$ using Chain Rule.



Somehow it can simplify further to: $6x^2(x+4)(x+8)^2$.



I can't manage the steps to get it to the simplified form.






calculus derivatives exponential-function







share|cite|improve this question




















  • 3




    Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
    – TheSimpliFire
    Nov 29 at 19:33














0












0








0







I found the derivative of $[x^3(x+8)^3]$ to equal $3x^2(x+8)^3+3x^3(x+8)^2$ using Chain Rule.



Somehow it can simplify further to: $6x^2(x+4)(x+8)^2$.



I can't manage the steps to get it to the simplified form.






calculus derivatives exponential-function







share|cite|improve this question















I found the derivative of $[x^3(x+8)^3]$ to equal $3x^2(x+8)^3+3x^3(x+8)^2$ using Chain Rule.



Somehow it can simplify further to: $6x^2(x+4)(x+8)^2$.



I can't manage the steps to get it to the simplified form.






calculus derivatives exponential-function




calculus derivatives exponential-function






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 29 at 19:34









TheSimpliFire

11.9k62257




11.9k62257










asked Nov 29 at 19:28









pijoborde

376




376








  • 3




    Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
    – TheSimpliFire
    Nov 29 at 19:33














  • 3




    Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
    – TheSimpliFire
    Nov 29 at 19:33








3




3




Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
– TheSimpliFire
Nov 29 at 19:33




Note that $3x^2y^3+3x^3y^2=3x^2y^2(y+x)$ and in this case $y=x+8$.
– TheSimpliFire
Nov 29 at 19:33










1 Answer
1






active

oldest

votes


















3














Carry out continuous factorizations, as :



$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2Big[(x+8)^3+x(x+8)^2Big] $$
$$=$$
$$3x^2(x+8)^2Big[x+8 + xBig] = 3x^2(x+8)^2(2x+8) $$
$$=$$
$$boxed{6x^2(x+4)(x+8)^2}$$






share|cite|improve this answer























  • Know anywhere I could read up on this??
    – pijoborde
    Nov 29 at 20:26










  • @pijoborde What do you mean ? You just factor out equal terms.
    – Rebellos
    Nov 29 at 20:27










  • Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
    – pijoborde
    Nov 29 at 20:34










  • Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
    – Rebellos
    Nov 29 at 20:40










  • thank you so much. That helped a lot being able to read along. Thank you.
    – pijoborde
    Nov 29 at 20:48











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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3














Carry out continuous factorizations, as :



$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2Big[(x+8)^3+x(x+8)^2Big] $$
$$=$$
$$3x^2(x+8)^2Big[x+8 + xBig] = 3x^2(x+8)^2(2x+8) $$
$$=$$
$$boxed{6x^2(x+4)(x+8)^2}$$






share|cite|improve this answer























  • Know anywhere I could read up on this??
    – pijoborde
    Nov 29 at 20:26










  • @pijoborde What do you mean ? You just factor out equal terms.
    – Rebellos
    Nov 29 at 20:27










  • Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
    – pijoborde
    Nov 29 at 20:34










  • Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
    – Rebellos
    Nov 29 at 20:40










  • thank you so much. That helped a lot being able to read along. Thank you.
    – pijoborde
    Nov 29 at 20:48
















3














Carry out continuous factorizations, as :



$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2Big[(x+8)^3+x(x+8)^2Big] $$
$$=$$
$$3x^2(x+8)^2Big[x+8 + xBig] = 3x^2(x+8)^2(2x+8) $$
$$=$$
$$boxed{6x^2(x+4)(x+8)^2}$$






share|cite|improve this answer























  • Know anywhere I could read up on this??
    – pijoborde
    Nov 29 at 20:26










  • @pijoborde What do you mean ? You just factor out equal terms.
    – Rebellos
    Nov 29 at 20:27










  • Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
    – pijoborde
    Nov 29 at 20:34










  • Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
    – Rebellos
    Nov 29 at 20:40










  • thank you so much. That helped a lot being able to read along. Thank you.
    – pijoborde
    Nov 29 at 20:48














3












3








3






Carry out continuous factorizations, as :



$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2Big[(x+8)^3+x(x+8)^2Big] $$
$$=$$
$$3x^2(x+8)^2Big[x+8 + xBig] = 3x^2(x+8)^2(2x+8) $$
$$=$$
$$boxed{6x^2(x+4)(x+8)^2}$$






share|cite|improve this answer














Carry out continuous factorizations, as :



$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2Big[(x+8)^3+x(x+8)^2Big] $$
$$=$$
$$3x^2(x+8)^2Big[x+8 + xBig] = 3x^2(x+8)^2(2x+8) $$
$$=$$
$$boxed{6x^2(x+4)(x+8)^2}$$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Nov 29 at 20:37

























answered Nov 29 at 19:31









Rebellos

14.2k31244




14.2k31244












  • Know anywhere I could read up on this??
    – pijoborde
    Nov 29 at 20:26










  • @pijoborde What do you mean ? You just factor out equal terms.
    – Rebellos
    Nov 29 at 20:27










  • Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
    – pijoborde
    Nov 29 at 20:34










  • Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
    – Rebellos
    Nov 29 at 20:40










  • thank you so much. That helped a lot being able to read along. Thank you.
    – pijoborde
    Nov 29 at 20:48


















  • Know anywhere I could read up on this??
    – pijoborde
    Nov 29 at 20:26










  • @pijoborde What do you mean ? You just factor out equal terms.
    – Rebellos
    Nov 29 at 20:27










  • Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
    – pijoborde
    Nov 29 at 20:34










  • Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
    – Rebellos
    Nov 29 at 20:40










  • thank you so much. That helped a lot being able to read along. Thank you.
    – pijoborde
    Nov 29 at 20:48
















Know anywhere I could read up on this??
– pijoborde
Nov 29 at 20:26




Know anywhere I could read up on this??
– pijoborde
Nov 29 at 20:26












@pijoborde What do you mean ? You just factor out equal terms.
– Rebellos
Nov 29 at 20:27




@pijoborde What do you mean ? You just factor out equal terms.
– Rebellos
Nov 29 at 20:27












Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
– pijoborde
Nov 29 at 20:34




Would you be willing to edit in the steps with words as you factored them out? I am not seeing it at this time.
– pijoborde
Nov 29 at 20:34












Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
– Rebellos
Nov 29 at 20:40




Well, first of all we see that we have $3x^2$ and $3x^3= 3x^2 cdot x$. So we factor out $3x^2$ and the rest remain the same. Then we have $(x+8)^2$ and $(x+8)^3 = (x+8)^2 cdot (x+8)$ and thus we factor out $(x+8)^2$. Then, we carry out the operations left in the parentheses and factor out $2$, since $2x+8 = 2(x+4)$.
– Rebellos
Nov 29 at 20:40












thank you so much. That helped a lot being able to read along. Thank you.
– pijoborde
Nov 29 at 20:48




thank you so much. That helped a lot being able to read along. Thank you.
– pijoborde
Nov 29 at 20:48


















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