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KonstantinChe [14]
3 years ago
15

Expand using pascal triangle (3x+2)^4

Mathematics
1 answer:
Liula [17]3 years ago
6 0

Answer:

The answer is

<h3>81x⁴ + 216x³ + 216x² + 94x + 16</h3>

Step-by-step explanation:

(3x + 2)⁴

<u>Using the Pascal's triangle</u>

For an exponent of 4 we have

( a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b³

Using a = 3x and b = 2 we have

( 3x +2)⁴ = ( 3x)⁴ + 4 [ (3x)³(2) ] + 6[ (3x)²(2)²] + 4 [ 3x(2)³ ] + 2⁴

Expand and simplify

That's

➢ ( 3x +2)⁴ = 81x⁴ + 4[ (27x³)(2) ] + 6 [ (9x²)(4) ] + 4 [ 3x(8) ] + 16

➢ 81x⁴ 4( 54x³) + 6(36x²) + 4( 24x) + 16

We have the final answer as

<h3>81x⁴ + 216x³ + 216x² + 94x + 16</h3>

Hope this helps you

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lina2011 [118]

Answer:

Jack

Step-by-step explanation:

90/18 = 5

180/45 = 4

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3 years ago
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A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it c
777dan777 [17]

Answer:

1250 ft^{2}

Step-by-step explanation:

We are given that the playground is fenced on three sides of the playground and the four side has an existing wall.

Let the length of the rectangle be 'X' feet and width be 'Y' feet.

As the fencing is done using 100 feet of fence. We get the relation between the sides and the fence as, X + 2Y = 100.

As, X + 2Y = 100 → X = 100 - 2Y

Now, the area of the rectangle = XY = X × ( 100 - 2Y ).

i.e Area of the rectangle = -2Y^{2} +100Y.

The general form of a quadratic equation is y=ax^{2}+bx+c.

The maximum value of a quadratic equation is given by x=\frac{-b}{2a}.

Therefore, the greatest value of -2Y^{2} +100Y is at Y = \frac{-100}{2 \times -2} = \frac{-100}{-4} = 25.

Thus, Y = 25 and X = 100 - 2Y → X = 100 - 2 × 25 → X = 50.

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3 years ago
Solve for x 6-12x = -54
kvasek [131]

Answer:

The answer of the question is 5

8 0
3 years ago
Algebra II, DOUBLE POINTS ! please help !!
bagirrra123 [75]

Answer:

the width is ≤ 38 feet

Step-by-step explanation:

the perimeter of a rectangle is given by the relation : 2*( length + width)

P ≤ 120

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3 years ago
Solve for a and b<br> (6a-3)=(7b-10)
Free_Kalibri [48]

Answer:

for A=\frac{7b-7}{6} and for B=\frac{6a+7}{7}

Step-by-step explanation:

For A

\left(6a-3\right)=\left(7b-10\right)

6a-3+3=7b-10+3

6a=7b-7

\frac{6a}{6}=\frac{7b}{6}-\frac{7}{6}

a=\frac{7b-7}{6}

For B

\left(6a-3\right)=\left(7b-10\right)

7b-10=\left(6a-3\right)

7b-10=6a-3

7b-10+10=6a-3+10

7b=6a+7

\frac{7b}{7}=\frac{6a}{7}+\frac{7}{7}

b=\frac{6a+7}{7}

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3 years ago
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