simplify 7pq^2 - 5pq( 2 -q). what are the steps

Question

Simplify.

 

^{7pq^2 - 5pq(2-q)}

Answer 1

The first step is to distribute what you can.

 

7pq² – 5pq(2–q) = 

 

7pq² –5pq*2 –5pq*(–q) =

 

7pq² –10pq + 5pq²  <= notice that q*q = q2 and the (-)*(-) gives a positive answer.

 

Now that you only have addition/subtraction, collect like terms. You have pq² and pq terms, which are apples and oranges, so collect the pq² terms together and leave the lone pq term alone.

 

7pq² –10pq + 5pq² =

 

12pq² - 10pq

 

At this point, you can either leave that alone, or factor out common terms... that depends on what your teacher expects here.

 

If you factor out common terms, you should realize that 12 and 10 are multiples of 2, so you can factor 2 out. Also both terms contain one p and one q, so you can factor those out too... so in essence, you can factor 2pq from each term.

 

12pq² - 10pq = 

 

2pq(6q) - 2pq(5) =

 

2pq(6p-5)

 

 

 

Answer 2

First we are going to need to distribute -5pq(2 - q):

-10pq + 5pq²

7pq² + 5pq² = 12pq²

 

And so we have:

12pq² - 10pq