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3 years ago

(a + b)³-(a - b)³- 6a²b

Mathematics

2 answers:

maksim [4K]3 years ago

7 0

Step-by-step explanation:

$(a + b)^{3} - (a - b)^{3} - 6 {a}^{2} b \\ a ^{3} + 3a ^{2} b + 3ab ^{2} + b ^{3} - (a ^{3} - 3a ^{2} b + 3ab ^{2} - b ^{3}) - 6 {a}^{2} b \\ a ^{3} + 3a ^{2} b + 3ab ^{2} + b ^{3} - a ^{3} + 3a ^{2} b - 3ab ^{2} + b ^{3}) - 6 {a}^{2} b \\ 3a ^{2} b + b ^{3} + 3a ^{2} b + b ^{3} - 6 {a}^{2} b \\ 6 {a}^{2} b + 2b ^{3} - 6 {a}^{2} b \\ 2b ^{3}$

Andru [333]3 years ago

3 0

Answer:

2b^3

Step-by-step explanation:

$(a+b)^3=a^3+b^3+3ab(a+b)\\(a-b)^3=a^3-b^3-3ab(a-b)\\(a+b)^3-(a-b)^3-6a^2b\\=a^3+b^3+3ab(a+b)-[a^3-b^3-3ab(a-b)]-6a^2b\\=2b^3$

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Vedmedyk [2.9K]

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Mazyrski [523]

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(1) At z=1.5, 2x^2 + 5y^2 + 1.5^2 = 4
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4 years ago

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frez [133]

Answer:

$P(x < 2.892) = 4.36\%$

Step-by-step explanation:

Given

$N = 700$ --- Population

$\mu = 2.894$ -- Mean

$\sigma = 0.009$ --- Standard deviation

$n = 55$ -- Sample

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$z = \frac{x - \mu}{\sqrt{\frac{N -n}{N -1}} * \frac{\sigma}{\sqrt n}}$

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$z = \frac{-0.002}{0.95917 * 0.0012129}$

$z = -1.71$

So:

$P(x < 2.892) = P(z < -1.71)$

Using z table

$P(x < 2.892) = 0.043633$

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