Sure! Let's simplify the expression step by step.
Given expression:
[tex]\[ 5(4c - 2d) + 2d - 6(d - 3) \][/tex]
Step 1: Distribute the constants inside the parentheses.
Distribute 5 in the first term:
[tex]\[ 5 \times 4c - 5 \times 2d = 20c - 10d \][/tex]
Distribute -6 in the last term (remember to keep track of the negative sign):
[tex]\[ -6 \times d + -6 \times -3 = -6d + 18 \][/tex]
Step 2: Rewrite the expression with the distributed terms.
Now, our expression looks like:
[tex]\[ 20c - 10d + 2d - 6d + 18 \][/tex]
Step 3: Combine like terms.
Combine the [tex]\(c\)[/tex] terms:
[tex]\[ 20c \][/tex]
Combine the [tex]\(d\)[/tex] terms:
[tex]\[ -10d + 2d - 6d = -10d + 2d - 6d = -14d \][/tex]
Finally, we include the constant term:
[tex]\[ 18 \][/tex]
Step 4: Write the simplified expression.
So, putting it all together, the simplified form of the expression is:
[tex]\[ 20c - 14d + 18 \][/tex]
This is the simplest form of the given expression.
