Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a) Simplify the expression and explain each step. 4[3x+2]-2
b) Factor the expression completely. 20b-16
@Leo Ok and?
a) To simplify the expression 4[3x+2]-2, we can use the distributive property.
First, let's distribute the 4 to both terms inside the brackets:
4 * 3x + 4 * 2 - 2
This gives us:
12x + 8 - 2
Next, we can simplify by combining like terms:
12x + 6
Therefore, the simplified expression is 12x + 6.
b) To factor the expression 20b-16, we can find the greatest common factor (GCF) of the two terms.
The GCF of 20b and 16 is 4, as it is the largest factor that divides evenly into both terms.
Now, let's factor out the GCF 4:
4(5b - 4)
Therefore, the completely factored expression is 4(5b - 4).
a) To simplify the expression 4[3x+2]-2, we need to apply the distributive property and then combine like terms.
First, we distribute the 4 to both terms inside the brackets:
4 * 3x = 12x
4 * 2 = 8
The expression now becomes:
12x + 8 - 2
Next, we combine like terms by adding 8 and -2:
12x + 6
Therefore, the simplified expression is 12x + 6.
b) To factor the expression 20b-16, we need to find the greatest common factor (GCF) of the terms and then factor it out.
First, let's identify the GCF of 20 and 16. The common factors of 20 and 16 are 1, 2, 4, and 8. However, the largest factor they both share is 4.
Now, we can factor out the GCF:
20b ÷ 4 = 5b
-16 ÷ 4 = -4
The expression now becomes:
4(5b - 4)
Therefore, the completely factored expression is 4(5b - 4).