Factorising (p+q)² + 5(p+q)

  • Thread starter thomas49th
  • Start date
In summary, the conversation discusses how to factorise the expression (p+q)^2 + 5(p+q) and the solution involves factoring out a common factor and using the distributive property to factorise further.
  • #1
thomas49th
655
0
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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  • #2
Both terms in the original problem have a common factor. Factor it out.
 
  • #3
If something is already factored for you (like (p+q)2 try not to multiply it again!
 
  • #4
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?
 
  • #5
There is one set of parentheses standing between you and a correct answer.
 
  • #6
[tex](p + q)(5 + p + q)[/tex]
 

1. What is factorising?

Factorising is the process of breaking down a mathematical expression into its simplest form by finding common factors.

2. How do I factorise a quadratic expression?

To factorise a quadratic expression, you can use the following steps:

  1. Identify the highest common factor of all terms in the expression.
  2. Use the distributive property to rewrite the expression as a product of the highest common factor and a simpler expression.
  3. Factorise the simpler expression by identifying common factors.
  4. Combine the factors to get the final factorised form.

3. How do I factorise (p+q)²?

To factorise (p+q)², you can use the following steps:

  1. Expand the expression using the FOIL method, which stands for First, Outer, Inner, Last.
  2. Simplify the expanded expression by combining like terms.
  3. Identify the highest common factor of all terms in the expression.
  4. Use the distributive property to rewrite the expression as a product of the highest common factor and a simpler expression.
  5. Factorise the simpler expression by identifying common factors.
  6. Combine the factors to get the final factorised form.

4. What is the purpose of factorising an expression?

Factorising can be useful in simplifying complicated expressions, solving equations, and finding solutions to real-life problems.

5. How do I factorise (p+q)² + 5(p+q)?

To factorise (p+q)² + 5(p+q), you can follow these steps:

  1. Identify the highest common factor of all terms in the expression, which in this case is (p+q).
  2. Use the distributive property to rewrite the expression as a product of the highest common factor and a simpler expression, which gives us (p+q)((p+q)+5).
  3. Factorise the simpler expression by identifying common factors, which gives us (p+q)(p+q+5).
  4. Combine the factors to get the final factorised form, which is (p+q)(p+5+q).

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