Mathematics
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OpenStudy (countrygirl1431):
Please help Algebra 2
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OpenStudy (countrygirl1431):
Perform the indicated operation.
OpenStudy (igreen):
Flip the 2nd fraction and multiply
OpenStudy (countrygirl1431):
@iGreen
OpenStudy (countrygirl1431):
\[\frac{ (a+3)^2 }{ a-3 }\times \frac{ a^2-9 }{5 }\]
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OpenStudy (igreen):
Correct, and can you multiply those 2 together?
OpenStudy (igreen):
Multiply the numerators together and multiply the denominators together.
OpenStudy (countrygirl1431):
im not sure how
OpenStudy (countrygirl1431):
i know it starts off \[2a^2\]
OpenStudy (igreen):
Okay, for the numerator we have \(\sf (a + 3)(a + 3)(a^2 - 9)\)
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OpenStudy (igreen):
Can you multiply \(\sf (a + 3)(a + 3)\)?
OpenStudy (countrygirl1431):
a+9
OpenStudy (igreen):
No..
\(\sf a \times a\)
\(\sf a \times 3\)
\(\sf 3 \times a\)
\(\sf 3 \times 3\)
Multiply those
OpenStudy (countrygirl1431):
im confused
OpenStudy (igreen):
\(\sf a \times a \rightarrow a^2\)
\(\sf a \times 3 \rightarrow 3a\)
\(\sf 3 \times a \rightarrow 3a\)
\(\sf 3 \times 3 \rightarrow 9\)
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OpenStudy (igreen):
Which gives us \(\sf a^2 + 6a + 9\), now multiply that to \(\sf a^2 - 9\)
OpenStudy (countrygirl1431):
ok i thought tht was it but i wasnt sure
OpenStudy (countrygirl1431):
so would this be a^4
OpenStudy (countrygirl1431):
or 6a^5
OpenStudy (igreen):
You gotta multiply all of them
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OpenStudy (igreen):
\(\sf a^2 \times a^2\)
\(\sf a^2 \times -9\)
\(\sf 6a \times a^2\)
\(\sf 6a \times -9\)
\(\sf 9 \times a^2\)
\(\sf 9 \times -9\)
OpenStudy (igreen):
The first one equals \(\sf a^4\), that's correct.
OpenStudy (countrygirl1431):
the 2nd 1 is a^2-9
OpenStudy (igreen):
No, it's \(\sf -9a^2\)
OpenStudy (countrygirl1431):
oh ok
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OpenStudy (countrygirl1431):
3=6a^3
OpenStudy (igreen):
Correct.
OpenStudy (countrygirl1431):
would 4 be -54a
OpenStudy (countrygirl1431):
5 wouldbt 9a^2 and 6 would be -81
OpenStudy (igreen):
4 is correct.
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OpenStudy (igreen):
So are 5 and 6.
OpenStudy (countrygirl1431):
ok
OpenStudy (igreen):
That gives us:
\(\sf a^4 - 9a^2 + 6a^3 - 54a + 9a^2 - 81\)
OpenStudy (igreen):
Combine like terms and you got:
\(\sf a^4 + 6a^3 - 54a - 81\)
OpenStudy (igreen):
Now simplify the denominator. \(\sf 5(a - 3)\)
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OpenStudy (countrygirl1431):
5a-3
OpenStudy (igreen):
Multiply 5 to both terms.
OpenStudy (igreen):
\(\sf 5 \times a\)
\(\sf 5 \times -3\)
OpenStudy (countrygirl1431):
5a and -15
OpenStudy (igreen):
Yes, that gives us:
\(\sf\dfrac{ a^4 + 6a^3 - 54a - 81}{5a - 15}
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OpenStudy (countrygirl1431):
i cant read it @green_1
OpenStudy (countrygirl1431):
@iGreen
OpenStudy (countrygirl1431):
sorry @green_1 i meant to tag someone else
OpenStudy (green_1):
you mean the equation above
OpenStudy (countrygirl1431):
the last thing posted i cant read it
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OpenStudy (countrygirl1431):
@iGreen could u repost the last thing