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 below
20b-16
a. 4(3x+2)-2 = 12x+8-2 = 12x+6.
both of these involve the distributive property. Looks like you need to review that topic.
4(3x+2 = 4*3x + 4*2 = 12x+8
20b-16 = 4*5b - 4*4 = 4(5b-4)
a) To simplify the expression 4(3x+2)-2, we can use the distributive property to eliminate the parentheses. We multiply 4 by every term inside the parentheses:
= 4 * 3x + 4 * 2 - 2
Simplifying the expression further:
= 12x + 8 - 2
= 12x + 6
b) To factor the expression 20b-16, we can start by finding the greatest common factor (GCF) of the two terms, which in this case is 4. We divide each term by the GCF:
= 4(5b - 4)
So, the factored expression is 4(5b - 4).
a) To simplify the expression 4(3x+2)-2, we can follow the order of operations (PEMDAS) and apply the distributive property.
Step 1: Distribute the 4 to each term inside the parentheses.
4(3x+2) - 2 = 12x + 8 - 2
Step 2: Combine like terms.
12x + 8 - 2 = 12x + 6
Therefore, the simplified expression is 12x + 6.
b) To factor the expression 20b - 16, we can look for a common factor.
Step 1: Identify the greatest common factor (GCF) of the terms.
In this case, the GCF is 4 because both 20 and 16 are divisible by 4.
Step 2: Divide each term by the GCF.
20b ÷ 4 = 5b
16 ÷ 4 = 4
Step 3: Write the factored expression.
20b - 16 = 4(5b - 4)
Therefore, the factored expression is 4(5b - 4).