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trapecia [35]
2 years ago
13

Find the third term in the expansion of (a+b)^9 in the simplest form

Mathematics
1 answer:
forsale [732]2 years ago
6 0

Answer:

The\ third\ term\ is\ \boxed{36a^7b^2}\\

Step-by-step explanation:

\left(\begin{array}{c}9\\ 1\end{array}\right)=\dfrac{9}{1} =9\\\\\left(\begin{array}{c}9\\ 2\end{array}\right)=\dfrac{9*8}{2*1} =36\\\\\\(a+b)^9=a^9+\left(\begin{array}{c}9\\ 1\end{array}\right)a^8b+\left(\begin{array}{c}9\\ 2\end{array}\right)a^7b^2+....+b^9\\\\\\The\ third\ term\ is\ \boxed{36a^7b^2}\\

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Which expression is equivalent to StartFraction (3 m Superscript negative 2 Baseline n) Superscript negative 3 Baseline Over 6 m
Dovator [93]

Option a: \frac{m^{5} }{162n} is the equivalent expression.

Explanation:

The expression is \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } where m\neq 0, n\neq 0

Let us simplify the expression, to determine which expression is equivalent from the four options.

Multiplying the powers, we get,

\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }

Cancelling the like terms, we have,

\frac{3^{-3}m^{5} n^{-1}}{6 }

This equation can also be written as,

\frac{m^{5}}{3^{3}6 n^{1} }

Multiplying the terms in denominator, we have,

\frac{m^{5} }{162n}

Thus, the expression which is equivalent to \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } is \frac{m^{5} }{162n}

Hence, Option a is the correct answer.

8 0
3 years ago
Read 2 more answers
Use distributive property to write an equivalent expression. Use paper and pencil to
just olya [345]

Answer:

A) 6Gn + 12 (or 6n+12, if that’s what you meant)

B) 4p²+9p

C) 5r²+20r

Step-by-step explanation:

A. If you meant 6(n+2)...

Multiply 6 by n and also 6 by 2:

6n + 12

B. Multiply p by 4p and also p by 9

4p²+9p

C. Multiply 5r by r and also 5r by 4

5r²+20r

Hope this helped!

8 0
3 years ago
What is 4+4-3+4-6+7=​
alina1380 [7]

Answer:

10

Step-by-step explanation:

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4 0
2 years ago
Geometry help please
bezimeni [28]

Answer:

x=2

ab=7

bc=5

Step-by-step explanation:

because you do

2x+3 = 4x+3

-3              -3

2x=4x

-2x -2x

x = 2

2x2+3

4+3

=7

4x2-3

8-3

=5

5 0
3 years ago
Read 2 more answers
A bag with 12 marbles has 3 red marbles and 5 yellow marbles. A marble is chosen from the bag at random. What is the probability
alexgriva [62]

Answer:

3/12 = 1/4

Step-by-step explanation:

There are 12 marbles in the bag.  If the marble drawn at random is red, it is one of the 3 red marbles.

The probability is "3 out of 12" = 3/12 which simplifies to 1/4.

7 0
3 years ago
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