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Temka [501]
3 years ago
10

Factor completely x3y6 – 64

Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0

Answer:

x 3 y 6 − 64

is the difference of two cubes and can be factored in the following pattern.

a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 )

a 3

factors to a

b 3

factors to b

The pattern of the signs follows the acronym SOAP

S = same sign as the cubes

O = opposite sins of the cubes

AP = always positive

x 3 y 3

factors to xy

64

factors to 4

x 3 y 3 − 64 = ( x y − 4 ) ( x 2 y 2 + 4 x y + 16 )

Step-by-step explanation:

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L = hours used by the Lopez's sprinkler

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so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.

likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.

we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.

we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.

\bf \begin{cases}
L+R=45\implies \boxed{L}=45-R\\
15L+40R=1050\\
----------\\
15\left(\boxed{45-R}  \right)+40R=1050
\end{cases}
\\\\\\
675-15R+40R=1050\implies 25R=375\implies R=\cfrac{375}{25}\\\\\\ R=15

how long was the Lopez's on for?  well, L = 45 - R.
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