How Do You Factorize (p+q)² + 5(p+q)?

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Homework Help Overview

The discussion revolves around the factorization of the expression (p+q)² + 5(p+q), which falls under algebraic manipulation and polynomial factorization.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the factorization of the expression, with some attempting to expand it first before factoring. There are questions about the appropriateness of multiplying out terms that are already factored.

Discussion Status

Some participants have suggested factoring out common terms, while others have attempted to rearrange the expression. There is an indication that progress is being made towards a factorized form, but no consensus has been reached on the final expression.

Contextual Notes

Participants are navigating the challenge of factoring an expression that includes terms that are already in a factored form, which raises questions about the approach to take.

thomas49th
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Relevant equations

Factorise
[tex](p+q)^{2}+5(p+q)[/tex]


The attempt at a solution

Multiply out the brackets giving

p² + q² +2pq + 5p + 5q

now how do I factorise that?

Thx
 
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Both terms in the original problem have a common factor. Factor it out.
 
If something is already factored for you (like (p+q)2 try not to multiply it again!
 
so i need to factorise the factorised. Hmmm. Well p + q is in each bracket so ill put that on the outside

[tex]p + q(5 + p + q)[/tex]

is that right?
 
There is one set of parentheses standing between you and a correct answer.
 
[tex](p + q)(5 + p + q)[/tex]
 

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