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2 years ago

Simplify (x + y)² - (x - y)² + 2xy - 3x²

Mathematics

1 answer:

Vinil7 [7]2 years ago

3 0

Answer:

$\huge\boxed{\sf 6xy-3x^2}$

Step-by-step explanation:

Given Expression:

(x + y)² - (x - y)² + 2xy - 3x²

Formulas used:

$(x+y)^2=x^2+2xy+y^2$
$(x-y)^2=x^2-2xy+y^2$

Expand the above expression according to the formulas

$=x^2+2xy+y^2-(x^2-2xy+y^2)+2xy-3x^2\\\\= x^2+2xy+y^2-x^2+2xy-y^2+2xy-3x^2\\\\cancel \ out \ x^2 \ and \ y^2\\\\= 2xy+2xy+2xy-3x^2\\\\= 6xy-3x^2\\\\\rule[225]{225}{2}$

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2 years ago

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a) The probability that the next house will be contacted and refuse to cooperate is 0.378

b) The probability of failing to contact a house, or making contact and not getting them to agree to the interview is 0.778

c) The probability of failing to contact a house, or making contact and not getting them to agree to the interview is the sum of both probabilities:

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2. the probability of making contact and not getting them to agree to the interview. It is equal to 0.378

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Step-by-step explanation:

From the question we know that interviewers reach 60% of the households and from those who are contacted, 37% is agree to cooperate with the survey. That's mean that the 63% of the reached household refuse to cooperate.

So the probability that the next house will be contacted and refuse to cooperate can be calculate as:

P= 0.6  *  0.63 = 0.378

Reach the households and refuse to cooperate

For part b, we need to identify and sum 2 independent probabilities:

1. the probability of failing to contact a house

2. the probability of making contact and not getting them to agree to the interview.

From part a we know that 0.378 is the probability of making contact and not getting them to agree to the interview.

Additionally, the probability of failing to contact a house is 0.4 because this probability is the complement of the probability of reach a household. This is calculate as:

1-0.6=0.4

Then the probability of failing to contact a house, or making contact and not getting them to agree to the interview is the sum of both probabilities:

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3 years ago

Simplify (x + y)² - (x - y)² + 2xy - 3x²​

Simplify (x + y)² - (x - y)² + 2xy - 3x²