Question 456713
{{{5b^4c^7d^6 - 7b^5c^3d^8}}}
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There are 2 terms.  Look for common factors. Both have b, c & d, so factor that out.
= {{{bcd*(5b^3c^6d^5 - 7b^4c^2d^7)}}}
Both terms still have bcd, so do it again.
= {{{b^2c^2d^2*(5b^2c^5d^4 - 7b^3cd^6)}}}
And again
= {{{b^3c^3d^3*(5bc^4d^3 - 7b^2d^5)}}}
Now the 2nd term has no "c", so factor out bd
= {{{b^4c^3d^4*(5c^4d^2 - 7bd^4)}}}
Only d is common to both now.  Factor out d^2, save a step
= {{{b^4c^3d^6*(5c^4 - 7bd^2)}}}
-----------------------------  That's all.
Doing it like that is tedious and time consuming.  Here's a different approach:
{{{5b^4c^7d^6 - 7b^5c^3d^8}}}
The highest exponent of b is 4.  Of c is 3, and of d is 6.
--> {{{b^4c^3d^6}}}
Divide the 2 terms by that.
= {{{b^4c^3d^6 * (5c^4 - 7bd^2)}}}