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C3 Differentiation Simplifying expressions help

I get how to use the different rules however I'm not sure what the heck is going on when I need to factorise my expression. For example:

4x2(2x+1)50 + 2x(2x+1)51

It apparently simplifies to:

x(2x+1)50(4x+1)

HOW?!

(See attachment for better layout of questions)

Please help me :frown:
help.png22.8KB
Reply 1
Avatar for Notnek
Notnek
21
Original post by lucaT
I get how to use the different rules however I'm not sure what the heck is going on when I need to factorise my expression. For example:

4x2(2x+1)50 + 2x(2x+1)51

It apparently simplifies to:

x(2x+1)50(4x+1)

HOW?!

(See attachment for better layout of questions)

Please help me :frown:

Think back to when you first learnt how to factorise:

4x2(2x+1)50+2x(2x+1)514x^2(2x+1)^{50} + 2x(2x+1)^{51}

What are the common factors of each of the two terms? You can take these "outside the bracket".


If you're still unsure, try factorising this

4x2y50+2xy514x^2y^{50} + 2xy^{51}

then realise that y=(2x+1)y=(2x+1). Please post all your working if you get stuck.
Reply 2
Avatar for MR1999
MR1999
21
Original post by Notnek
Think back to when you first learnt how to factorise:

4x2(2x+1)50+2x(2x+1)514x^2(2x+1)^{50} + 2x(2x+1)^{51}

What are the common factors of each of the two terms? You can take these "outside the bracket".


If you're still unsure, try factorising this

4x2y50+2xy514x^2y^{50} + 2xy^{51}

then realise that y=(2x+1)y=(2x+1). Please post all your working if you get stuck.


I do believe there's a mistake. I think should be 2x(4x+1)(2x+1)502x(4x+1)(2x+1)^{50}
Reply 3
Avatar for Notnek
Notnek
21
Original post by Desmos
I do believe there's a mistake. I think should be 2x(4x+1)(2x+1)502x(4x+1)(2x+1)^{50}

Oops I didn't notice the mistake. This could be why the OP is confused.

Thanks :smile:
Reply 4
Avatar for lucaT
lucaT
OP
2
Original post by Notnek
Think back to when you first learnt how to factorise:

4x2(2x+1)50+2x(2x+1)514x^2(2x+1)^{50} + 2x(2x+1)^{51}

What are the common factors of each of the two terms? You can take these "outside the bracket".


If you're still unsure, try factorising this

4x2y50+2xy514x^2y^{50} + 2xy^{51}

then realise that y=(2x+1)y=(2x+1). Please post all your working if you get stuck.


Thank you, I'm using 4x2y50+2xy514x^2y^{50} + 2xy^{51} if I get too stuck now

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