How do you factor #2c^2d-4c^2d^2#?

2 Answers
Mar 22, 2018

Answer:

#2c^2d(1-2d)#

Explanation:

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)#

Mar 22, 2018

Answer:

#(2c^2d)(1-2d)#

Explanation:

#{: ("terms:",2c^2d,-,4c^2d^2), ("factors:",1xx2xxcxxcxxd,,1xx2xx2xxcxxcxxd xxd), ("common factors (excluding 1):",color(lime)(color(white)(1xx)2xxcxxcxxd)-,,color(lime)(1xx2color(white)(xx2)xxcxxcxxdcolor(white)( xxd))), ("remaining factors:",color(blue)(1color(white)(xx2xxcxxcxxd)),-,color(magenta)(color(white)(1xx2xx)2color(white)(xxcxxcxxd) xxd)) :}#

#2c^2d-4x^2d^2#

#color(white)("XXX")=color(lime)(""(2xxcxxcxxd)) xx (color(blue)1 - color(magenta)(""(2xxd)))#

#color(white)("XXX")=color(lime)(""(2c^2d))color(purple)(""(1-2d))#