Alright, let's work through the given expression step-by-step to expand and simplify it fully.
We start with the expression:
[tex]\[ 2(w - 1) + 5(2w + 3) \][/tex]
First, we'll distribute the constants 2 and 5 through the parentheses.
For the first term [tex]\(2(w - 1)\)[/tex]:
[tex]\[ 2 \times w + 2 \times (-1) = 2w - 2 \][/tex]
For the second term [tex]\(5(2w + 3)\)[/tex]:
[tex]\[ 5 \times 2w + 5 \times 3 = 10w + 15 \][/tex]
Now, we have the expression expanded:
[tex]\[ 2w - 2 + 10w + 15 \][/tex]
Next, we combine like terms. We will add together the terms that contain [tex]\(w\)[/tex] and the constant terms.
Combine the [tex]\(w\)[/tex] terms:
[tex]\[ 2w + 10w = 12w \][/tex]
Combine the constant terms:
[tex]\[ -2 + 15 = 13 \][/tex]
So, when we put it all together, the fully simplified expression is:
[tex]\[ 12w + 13 \][/tex]
Therefore, the expanded and fully simplified form of the given expression [tex]\( 2(w - 1) + 5(2w + 3) \)[/tex] is:
[tex]\[ 12w + 13 \][/tex]
