How do you factor $a c + 2 a d + 2 b c + 4 b d$ $ac + 2ad + 2bc + 4bd$ ?

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How do you factor $a c + 2 a d + 2 b c + 4 b d$ $ac + 2ad + 2bc + 4bd$ ?

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Answer 1 · 2015-06-30T12:11:22

$(c + 2 d) (a + 2 b)$ $(c+2d)(a+2b)$

Explanation:

In other factorize, we need to take out common factors.
We have here;
$a c + 2 a d + 2 b c + 4 b d$ $ac+2ad+2bc+4bd$
Take out $a$ $a$ as a common factor from first two variables and $2 b$ $2b$ from last two variables, we get;
$= a (c + 2 d) + 2 b (c + 2 d)$ $=a(c+2d)+2b(c+2d)$
Now, again take out $(c + 2 d)$ $(c+2d)$ as a common factor, we get
$= (c + 2 d) (a + 2 b)$ $=(c+2d)(a+2b)$
This is our final answer.

Answer 2 · 2015-06-30T12:13:14

$a c + 2 a d + 2 b c + 4 b d$ $ac+2ad+2bc+4bd$
$XXXX$ $color(white)("XXXX")$ $= (a + 2 b) (c + 2 d)$ $=(a+2b)(c+2d)$

Explanation:

Given $a c + 2 a d + 2 b c + 4 b d$ $ac+2ad+2bc+4bd$

Regroup as
$XXXX$ $color(white)("XXXX")$ $(a c + 2 a d) + (2 b c + 4 b d)$ $color(red)((ac+2ad)) + color(blue)((2bc+4bd))$

Extract common factor from each term independently
$XXXX$ $color(white)("XXXX")$ $(a) (c + 2 d) + (2 b) (c + 2 d)$ $color(red)((a)(c+2d)) + color(blue)((2b)(c+2d))$

Extract the factor common to both terms
$XXXX$ $color(white)("XXXX")$ $(a + 2 b) (c + 2 d)$ $(color(red)(a)+color(blue)(2b))(c+2d)$

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How do you factor $a c + 2 a d + 2 b c + 4 b d$ $ac + 2ad + 2bc + 4bd$ ?

2 Answers

Explanation:

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How do you factor ac+2ad+2bc+4bdac + 2ad + 2bc + 4bd?

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How do you factor $a c + 2 a d + 2 b c + 4 b d$ $ac + 2ad + 2bc + 4bd$ ?