To factor the expression [tex]\(210d^2 - 63d\)[/tex], follow these steps:
1. Identify Common Factors:
Examine the coefficients (210 and 63) and the variable for common factors:
[tex]\[ 210 = 2 \times 3 \times 5 \times 7 \][/tex]
[tex]\[ 63 = 3 \times 3 \times 7 \][/tex]
The common factors of 210 and 63 are [tex]\(3 \times 7 = 21\)[/tex].
The common variable factor is [tex]\(d\)[/tex].
2. Factor Out the GCD:
Since both terms share a common factor of [tex]\(21d\)[/tex], we can factor that out:
[tex]\[ 210d^2 - 63d = 21d(10d) - 21d(3) \][/tex]
3. Factor Each Term:
When the common factor [tex]\(21d\)[/tex] is factored out, distribute it across the remaining terms:
[tex]\[ 21d(10d - 3) \][/tex]
Therefore, the factored form of [tex]\(210d^2 - 63d\)[/tex] is:
[tex]\[
21d(10d - 3)
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{21d(10d - 3)}
\][/tex]
This corresponds to option F in the given choices.
