Ishaan Mcneil

2022-02-09

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

arrejuntam58

Beginner2022-02-10Added 11 answers

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:

$2{x}^{3}{y}^{5}(6{x}^{7-3}{y}^{9-5}+3{x}^{4-3}{y}^{7-5}-5{x}^{3-3}{y}^{5-5})\Rightarrow$

$2{x}^{3}{y}^{5}(6{x}^{4}{y}^{4}+3{x}^{1}{y}^{2}-5{x}^{0}{y}^{0})\Rightarrow$

$2{x}^{3}{y}^{5}(6{x}^{4}{y}^{4}+3x{y}^{2}-5\cdot 1\cdot 1)\Rightarrow$

$2{x}^{3}{y}^{5}(6{x}^{4}{y}^{4}+3x{y}^{2}-5)$

For the constants 12, 6 and 10 the highest common value is 2

For x the highest common value is

For y the highest common value is

So, we can rewrite this problem, using the rules for exponents as:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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