How do you factor $2 c^{2} d - 4 c^{2} d^{2}$ $2c^2d-4c^2d^2$ ?

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How do you factor $2 c^{2} d - 4 c^{2} d^{2}$ $2c^2d-4c^2d^2$ ?

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Answer 1 · 2018-03-22T12:56:16

$2 c^{2} d (1 - 2 d)$ $2c^2d(1-2d)$

Explanation:

We start with:

$\Rightarrow 2 c^{2} d - 4 c^{2} d^{2}$ $=>2c^2d-4c^2d^2$

Next, we identify terms that are similar:

$\Rightarrow 2 c^{2} d - 4 c^{2} d^{2}$ $=>color(orange)(2)color(blue)(c^2)color(red)(d)-color(orange)(4)color(blue)(c^2)color(red)(d^2)$

Let's start with $orange$ $color(orange)"orange"$ . We have $2$ $2$ and $4$ $4$ on opposite sides of the minus sign. The greatest common factor of these two values is $2$ $2$ , so that is what we factor out first. This will leave a $2$ $2$ on the RHS of the minus sign.

$\Rightarrow 2 (c^{2} d - 2 c^{2} d^{2})$ $=>color(orange)(2)(color(blue)(c^2)color(red)(d)-color(orange)(2)color(blue)(c^2)color(red)(d^2))$

Now let's look at $blue$ $color(blue)"blue"$ . We have the same term $c^{2}$ $c^2$ on both sides of the minus sign. So we can factor this term out.

$\Rightarrow 2 c^{2} (d - 2 d^{2})$ $=>2color(blue)(c^2)(color(red)(d)-2color(red)(d^2))$

Now the last type of term is $red$ $color(red)"red"$ . We have one term with a power of $1$ $1$ and one term with a power of $2$ $2$ . With powers, we factor out the lowest power $L$ $L$ . Any terms with a power higher (say $H$ $H$ ) than the lowest will be leftover with a power equal to $H - L$ $H-L$ . Let's factor out $d$ $d$ . Note! The term on the LHS of the minus sign will become $1$ $1$ , since there are no other terms left after factoring.

$\Rightarrow 2 c^{2} d (1 - 2 d)$ $=>2c^2color(red)(d)(1-2color(red)(d))$

Now that we have touched all of the terms, we are finished. The factored version of the expression is:

$\Rightarrow 2 c^{2} d (1 - 2 d)$ $=>2c^2d(1-2d)$

Answer 2 · 2018-03-22T13:10:20

$(2 c^{2} d) (1 - 2 d)$ $(2c^2d)(1-2d)$

Explanation:

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

$2c^2d-4x^2d^2$

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

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

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How do you factor $2 c^{2} d - 4 c^{2} d^{2}$ $2c^2d-4c^2d^2$ ?

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Explanation:

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