a) Simplify the expression and explain each step.
4(3x + 2) - 2
b) Factor the expression completely.
20b - 16
I'm not asking for answers. I just want help figuring out what the letters in the equation mean. Thanks!
a) 12x + 8 - 2 = ?
b Factor out 4.
Is psydag right?
12x+(8-2) = 12x+6
For the second question, we first find the GCF. To do this, find the prime factorization of 20 and 16:
20 = 4*5
4 = 2*2
20 = 2*2*5
16 = 4*4
4 = 2*2
16 = 2*2*2*2
For the GCF, we take the common factors; these are 2*2 = 4. This makes 4 the GCF.
Factoring 4 out of 20b, we have 5b; factoring 4 out of -16 gives us -4. This gives us 4(5b-4).
a) Let's simplify the expression 4(3x + 2) - 2 step by step.
Step 1: Distribute
To distribute means to multiply each term inside the parentheses by the number outside the parentheses. In this case, the number outside the parentheses is 4.
So, we can rewrite the expression as:
4 * 3x + 4 * 2 - 2
Step 2: Simplify the terms inside parentheses
The first term inside the parentheses is 3x, and the second term is 2. Since there is no operation between them, we assume that there is an invisible addition sign. So, we can rewrite the expression as:
12x + 8 - 2
Step 3: Simplify the remaining terms
Now, we combine like terms. In this case, 8 and -2 are like terms, which means they both represent constant values without variables. So, we can add them together:
12x + 6
b) Let's factor the expression 20b - 16 completely.
To factor means to express an expression as a product of its factors. In this case, we want to find two numbers or terms that can be multiplied to give us the original expression.
Step 1: Find the greatest common factor (GCF)
The GCF is the largest number or term that divides evenly into all the terms of the expression. In this case, the GCF is 4. We can factor it out:
4 * (5b - 4)
Step 2: Simplify the expression inside parentheses
The expression (5b - 4) does not have any common factors, so it cannot be factored further.
Therefore, the completely factored expression is:
4(5b - 4)