10a) Simplify the expression and explain each step.
12 + 3(2y – 3)
Step 1: apply distributive property
Step 2: combine like terms
Step 3: simplify
b) Factor the expression completely.
18b – 12
What is the GCF of 18 and 12? Use ladder method or listing.
1. a
2. c
3. b
4. d
5. a
6. d
7. d
8. c
9. d
10. For the first question, we first use the distributive property. It states that we multiply everything within parentheses by the term outside parentheses:4(3x+2)-2 = 4(3x)+4(2)-2 = 12x+8-2Combine like terms:12x+(8-2) = 12x+6For the second question, we first find the GCF. To do this, find the prime factorization of 20 and 16:20 = 4*54 = 2*220 = 2*2*516 = 4*44 = 2*216 = 2*2*2*2For 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).
for connexus
12 + 3(2y – 3)
12 + 6y - 9
3 + 6y
I did the first one. Now you can do the second one.
18b - 12 =?
10a) To simplify the expression 12 + 3(2y – 3), we follow these steps:
Step 1: Apply the distributive property.
We distribute the 3 to both terms inside the parentheses:
12 + 3 * 2y - 3 * 3
Step 2: Combine like terms.
We can simplify the expression by multiplying the coefficients and adding or subtracting any like terms. In this case, we have two terms with the variable y and one constant term:
12 + 6y - 9
Step 3: Simplify.
Finally, we can combine the constants and the variable term:
(12 - 9) + 6y
3 + 6y
So, the simplified expression is 3 + 6y.
b) To factor the expression 18b – 12 completely, we need to determine the greatest common factor (GCF) of 18 and 12.
To find the GCF, we can either use the ladder method or list the factors of each number.
Using the ladder method:
Starting with the two numbers 18 and 12, we divide both numbers by common prime factors until we can't divide anymore. The factors on the top row are the prime factors of 18, and the factors on the bottom row are the prime factors of 12.
18 | 2
|---------
9 | 2
|---------
3 | 3
The prime factors of 18 are 2 * 3 * 3 = 18.
The prime factors of 12 are 2 * 2 * 3 = 12.
The GCF is the product of the common prime factors, which is 2 * 3 = 6.
So, the GCF of 18 and 12 is 6.
To factor the expression completely, we can factor out the GCF from both terms:
6(3b - 2).
Therefore, the expression 18b – 12 can be completely factored as 6(3b - 2).