# Factor by the method of grouping. Show the check by re-multiplication of the factors. 10xy-2xy+45x-9w

Factor by the method of grouping. Show the check by re-multiplication of the factors.
$10xy-2xy+45x-9w$
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Given equation is
$10xy-2xy+45x-9w$
Above equation rewritten as
$10xy+45x-2xy-9x=5x\left(2y+9\right)-x\left(2y+9\right)\phantom{\rule{0ex}{0ex}}=\left(5x-x\right)\left(2y-9\right)\phantom{\rule{0ex}{0ex}}=4x\left(2y+9\right)$
Factors are
Or,
So, we get
$10xy-2xy+45x-9x=8xy+36x$
Multiply the factors (4x) and (2y+9) we get
$\left(4x\right)\left(2y+9\right)=4x×2y+4x×9\phantom{\rule{0ex}{0ex}}=8xy+36x$
Then, we check multiplication of factors
Factors are 4x, 2y+9