Question

Find the greatest common factor of 6a^3b^2c^10 + 20c^10 – 8a^3b^2c^9

Answer 1

Answer:
`2c^9`

Explanation:

I'm assuming this is the expression:
`6a^3b^2c^(10)+\:20c^(10)\:-\:8a^3b^2c^9`

`\mathrm{Factor\:}6a^3b^2c^(10)` (Expand using 2's and 3's as they are the common factor in all terms)

`2\cdot \:3\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c`

`\mathrm{Factor\:}20c^(10)` (5 needed to expand the coefficient)

`2\cdot \:2\cdot \:5\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c`

`\mathrm{Factor\:}8a^3b^2c^9`

`2\cdot \:2\cdot \:2\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c`

Common factors (terms that are in all expressions):

`2\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c`

Simplify:

`2c^9`