Help Me Factorise: 3(n+r)(n+r-1) + (n+r) to (n+r)(3n+3r-2)

  • Thread starter confused88
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In summary, the conversation is about factoring an expression and the process of expanding and collecting like terms. The example provided helps to understand the concept better. The final result is achieved by substituting the original expression with a variable and then expanding and collecting like terms.
  • #1
confused88
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Can someone please help me with very simple math.. and explain slowly how they got from
3(n+r)(n+r-1) + (n+r)
to (n+r)(3n+3r-2)?

I forgot how to factorise, so can someone help me do this please?
 
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  • #2
The n+r is already factored out. Just write everything in terms of that and you'll see.

(It's actually easier to understand by doing, in this case, than to have it explained!)
 
  • #3
Explain slowly you say? Maybe that can be expressed through example.

ab+ac=a(b+c)
xy+x=x(y+1)
pqr+r=r(pq+1)

If you understand how to do the opposite of factorising which is expanding, then these results would be easy to confirm.

So for 3(n+r)(n+r-1) + (n+r)
let n+r=x
So we now have 3x(x-1)+x
Factorising x out: x(3(x-1)+1)
Expand 3(x-1) and collect like terms, then substitute n+r=x back into the result.
 
  • #4
Oh wow i get it now. Thank you!
 

FAQ: Help Me Factorise: 3(n+r)(n+r-1) + (n+r) to (n+r)(3n+3r-2)

What is factorisation?

Factorisation is the process of breaking down an expression or equation into smaller parts, called factors, that when multiplied together, give the original expression. It is the inverse operation of multiplication.

How do I factorise an expression?

To factorise an expression, you need to identify common factors and then use techniques such as the distributive property, grouping, or difference of squares to break down the expression into its factors.

What is the difference between factorising and simplifying?

Factorising and simplifying are two different processes. Factorising involves breaking down an expression into its factors, while simplifying involves simplifying an expression by performing mathematical operations to reduce it to its simplest form.

How do I factorise a quadratic expression?

To factorise a quadratic expression, you can use the following techniques: grouping, difference of squares, trial and error, or the quadratic formula. It is important to first check if the expression can be factored before attempting these techniques.

How can I check if my factorisation is correct?

You can check if your factorisation is correct by expanding the factors back to the original expression. If the expanded expression matches the original expression, then your factorisation is correct. You can also use the distributive property to check your factorisation.

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