Question

A) Simplify the expression and explain each step. (2 points)

4(3x + 2) – 2


b)  Factor the expression completely.  (1 point)


20b – 16

Answer 1

a) 4 (3x+2)-2
12x+8-2
12x+6
2x+1 simplified expression

Answer 2

a)
`4\left(3x+2\right)-2=12x+6`

b)
`20b-16= 4\left(5b-4\right)`

Explanation:

a) To simplify the expression you must:

Expand
`4(3x + 2)`:

Apply the distributive law:
`\:a\left(b+c\right)=ab+ac`

`a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2`

Simplify
`4\cdot \:3x+4\cdot \:2= 12x+8`

`12x+8-2`

Subtract the numbers:
`4\left(3x+2\right)-2=12x+6`

b) To factor the expression
`20b - 16` you must:

Rewrite 16 as
`4\cdot 4` and 20 as
`4\cdot 5`

`20b-16=4\cdot \:5b-4\cdot \:4`

Factor out common term 4

`20b-16= 4\left(5b-4\right)`