We start with:
#=>2c^2d-4c^2d^2#
Next, we identify terms that are similar:
#=>color(orange)(2)color(blue)(c^2)color(red)(d)-color(orange)(4)color(blue)(c^2)color(red)(d^2)#
Let's start with #color(orange)"orange"#. We have #2# and #4# on opposite sides of the minus sign. The greatest common factor of these two values is #2#, so that is what we factor out first. This will leave a #2# on the RHS of the minus sign.
#=>color(orange)(2)(color(blue)(c^2)color(red)(d)-color(orange)(2)color(blue)(c^2)color(red)(d^2))#
Now let's look at #color(blue)"blue"#. We have the same term #c^2# on both sides of the minus sign. So we can factor this term out.
#=>2color(blue)(c^2)(color(red)(d)-2color(red)(d^2))#
Now the last type of term is #color(red)"red"#. We have one term with a power of #1# and one term with a power of #2#. With powers, we factor out the lowest power #L#. Any terms with a power higher (say #H#) than the lowest will be leftover with a power equal to #H-L#. Let's factor out #d#. Note! The term on the LHS of the minus sign will become #1#, since there are no other terms left after factoring.
#=>2c^2color(red)(d)(1-2color(red)(d))#
Now that we have touched all of the terms, we are finished. The factored version of the expression is:
#=>2c^2d(1-2d)#
