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. (2 points)
4(3x+2)−2
b) Factor the expression completely. (1 point)
20b−16
the first steps are:
4*3x + 4*2 - 2
4*5b - 4*4
thanks, dude yo
a)
To simplify the expression 4(3x+2)−2, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
1. Distribute the 4 to each term inside the parentheses:
4 * 3x = 12x
4 * 2 = 8
So, the expression becomes 12x + 8 - 2.
2. Combine like terms:
12x + 8 - 2 = 12x + 6
Therefore, the simplified expression is 12x + 6.
b)
To factor the expression 20b−16, we need to look for common factors in both terms.
The greatest common factor of 20b and -16 is 4.
1. Divide each term by the greatest common factor:
20b / 4 = 5b
-16 / 4 = -4
So, the expression becomes 4(5b - 4).
Therefore, the factored form of the expression is 4(5b - 4).
a) Simplify the expression 4(3x+2)−2 step-by-step:
Step 1: Distribute 4 to each term inside the parentheses:
4 * 3x + 4 * 2 - 2
Which simplifies to:
12x + 8 - 2
Step 2: Combine like terms:
12x + 6
Thus, the simplified expression is 12x + 6.
b) Factor the expression 20b−16:
Step 1: Find the greatest common factor (GCF) of the terms:
The GCF of 20 and 16 is 4.
Step 2: Divide each term by the GCF:
20b/4 - 16/4
Which simplifies to:
5b - 4
This is the factored expression: 5b - 4.