Question

1. Simplify the expression and explain each step: 4(3x+2)-2.

Answer 1

1. 4 (3x+2)-2
distribute the 4 to 3x and 2
12x+8-2
combine like terms: 8-2
12x+6
answer: 12x+6

2. 20b - 16
/ \ / \
10 2 8 2
/ \ / \
5 2 4 2
/ \
2 2
answer: 5×2×2×b+2×2×2×2

Answer 2

The correct answers are:

12x+6; and 4(5b-4).

Explanation:

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+8-2

Combine like terms:

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).