simplify (6z+4y-2y)(z+5z-2y)

Question

how would i simplify this expression (6z+4y-2y)(z+5z-2y)

Answer 1

Usually, The basic steps are:

 

1. First simplify each expression in parentheses.  Do this by gathering the like terms.

 

2. The multiply each term in the first expression in parentheses by each term in the second expression. 

 

3. Gather all the like terms together

 

So the first expression is 6z+4y-2y = 6z + 2y

 

And the second expression is z+5z-2y = 6z - 2y

 

So you're multiplying (6z + 2y)(6z - 2y)

 

Now you can multiply each term in the first expression each term in the second expression

 

6z * 6z = 36z²

6z * (-2y) = -12zy

2y * 6z = 12zy

2y * (-2y) = -4y²

 

Add these together.  Notice that -12zy and 12zy cancel.  So you are left with 36z² - 4y²

 

 

HOWEVER...  You can also notice that (6z + 2y)(6z - 2y) is "a number PLUS a number" times "the first  number MINUS the second number".  That's just going to be the difference of the squares of the numbers.  (That's a trick about the difference between two squares that you'll want to remember.)  So the answer comes out to (6z)² - (2y)² = 36z² - 4y² .  Same answer without having to do all the multiplications.