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brilliants [131]
3 years ago
7

at%20%5C%3A%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%20%20%7By%7D%5E%7B3%20%7D%20%20%2B%20%20%7Bz%7D%5E%7B3%7D%20%20%3D%203xyz" id="TexFormula1" title="if \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} = 3xyz" alt="if \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} = 3xyz" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
elena-s [515]3 years ago
6 0

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3

⟹x 3 +y 3 +3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3 +y 3−3xyz=−z 3

⟹x 3 +y 3 +z 3 =3xyz

Step-by-step explanation:

Hope it is helpful.....

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Multiply the Polynomials:<br><br> (2x+3) (-x+2y-4)
GREYUIT [131]

The result of multiplying the polynomials is (2x + 3) (-x + 2y - 4) = -2x² + 4xy - 11x + 6y - 12

<h3>How to multiply the polynomials?</h3>

The polynomial expression is given as

(2x + 3) (-x + 2y - 4)

Expand the brackets in the above polynomial expression

So, we have

(2x + 3) (-x + 2y - 4) = 2x * (-x + 2y - 4) + 3 * (-x + 2y - 4)

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So, we have

(2x + 3) (-x + 2y - 4) = -2x² + 4xy - 8x + -3x + 6y - 12

Evaluate the like terms in the above polynomial expression

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Hence, the solution is -2x² + 4xy - 11x + 6y - 12

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2 years ago
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Mary has 200ml of hand sanitizer that is 15% alcohol. She mixes it with 200ml of a
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Answer:

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Step-by-step explanation:

We are given that

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