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3 years ago

Expand the following using either the Binomial Theorem You must show

1 answer:

n200080 [17]3 years ago

4 0

<h2><u><em>Answer:</em></u></h2><h2><em>A Pascal triangle is the triangular way of expanding a binomial. So the best way in expanding that function is thru Binomial Theorem and the expanded for of it is 8x^3+48x^2+98x+64 </em></h2><h2><em></em></h2><h2><u><em>Step-by-step explanation:</em></u></h2><h2><em>Before even trying to put this into the binomial form, we must figure out the coefficients. If we go by the Pascal's Triangles way we should end up with: </em></h2><h2><em> </em></h2><h2><em> 1 </em></h2><h2><em> </em></h2><h2><em> 1 1 </em></h2><h2><em> </em></h2><h2><em> 1 2 1 </em></h2><h2><em> </em></h2><h2><em>1 3 3 1 </em></h2><h2><em> </em></h2><h2><em>Going by the last level (which is the third level) we get 3C0:1, 3C1:3, 3C2:3, 3C3:1. </em></h2><h2><em> </em></h2><h2><em>Now with the equation: (a+b)^3 = 3C0a^3 + 3C1a^2 b + 3C2a b^2 + 3C3b^3 we just plug in all the values and simplify </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 2x^3 + 3(2x)^2 (4) + 3(2x) (4)^2 + (4)^3 </em></h2><h2><em> </em></h2><h2><em>(2x+4)^3 = 8x^3 + (3)(4x^2)(4) + (3)(2x)(16) + 64 </em></h2><h2><em> </em></h2><h2><em>Then we finally end with: (2x+4)^3 = 8x^3 48x^2 + 96x +64 </em></h2>

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Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

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timofeeve [1]

Answer:

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Elena-2011 [213]

The expressions that are equal to 61 are

|−61|
The distance from zero to −61
−(−61)
The opposite of −61

<h3>How to determine the expressions?</h3>

The value of the expression is given as:

Value = 61

Next, we evaluate the options:

<u>Option 1: |−61| </u>

The expression is given as:

Expression = |-61|

Remove the absolute sign

Expression = 61

Hence, |-61| equals 61

<u>Option 2: The distance from zero to −61 </u>

This is represented as:

Distance = |-61 - 0|

Evaluate the difference

Distance = |-61|

Remove the absolute sign

Distance = 61

Hence, the distance from zero to −61 is 61

<u>Option 3: The opposite of 61 </u>

The opposite of 61 is represented as:

Opposite = -(61)

Evaluate

Opposite = -61

Hence, the opposite of 61 is -61

<u>Option 4:−(−61) </u>

The expression is given as:

Expression = -(-61)

Remove the bracket

Expression = 61

Hence, -(-61) equals 61

<u>Option 5: the opposite of −61</u>

The opposite of -61 is represented as:

Opposite = -(-61)

Evaluate

Opposite = 61

Hence, the opposite of -61 is 61

<u>Option 6: −|−61| </u>

The expression is given as:

Expression = -|-61|

Remove the absolute sign

Expression = -61

Hence, -|-61| equals -61

<u>Option 6: −|61| </u>

The expression is given as:

Expression = -|61|

Remove the absolute sign

Expression = -61

Hence, -|61| equals -61