Ishaan Mcneil

2022-02-09

How do you factor $12{x}^{7}{y}^{9}+6{x}^{4}{y}^{7}-10{x}^{3}{y}^{5}$?

### Answer & Explanation

arrejuntam58

You need to pull the highest common value out of each variable and constant in the terms:
For the constants 12, 6 and 10 the highest common value is 2
For x the highest common value is ${x}^{3}$
For y the highest common value is ${y}^{5}$
So, we can rewrite this problem, using the rules for exponents as:
$2{x}^{3}{y}^{5}\left(6{x}^{7-3}{y}^{9-5}+3{x}^{4-3}{y}^{7-5}-5{x}^{3-3}{y}^{5-5}\right)⇒$
$2{x}^{3}{y}^{5}\left(6{x}^{4}{y}^{4}+3{x}^{1}{y}^{2}-5{x}^{0}{y}^{0}\right)⇒$
$2{x}^{3}{y}^{5}\left(6{x}^{4}{y}^{4}+3x{y}^{2}-5\cdot 1\cdot 1\right)⇒$
$2{x}^{3}{y}^{5}\left(6{x}^{4}{y}^{4}+3x{y}^{2}-5\right)$

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