a) Factor 9x² + y² + z² - 6xy + 2yz - 6xz
This looks a lot like
(x+y+z)² = x² + y² + z²+ 2xy + 2yz + 2xz
except instead of x there's (-3x). So this must be
(-3x+y+z)² = (-3x)² + y² + z² + 2((-3x)y + (-3x)z + yz)
= 9x² + y² + z² - 6xy + 2yz - 6xz
Looks good.
Answer: (-3x+y+z)²
Since it's a square we could also negate the inside and write this (3x-y-z)²
b) I'll guess that says we want to evaluate this when x=1, y=2, z= -1
(-3(1) + 2 -1)² = (-2)² = 4
Answer: 4
Answer:

Step-by-step explanation:
Using the rule of exponents
×
⇔
, thus
×
=
= 
Answer:
Step-by-step explanation:
Given that 10000 times a fair coin is flipped. Since fair coin prob for head of tail =0.5
If tail comes it will be taken as 1. Hence for the sum to be less than 5000, no of heads <5000
Since trials are large we approximate to normal with mean = np = 5000 and variance = np(1-p) = 2500
Thus no of heads x is normal with (5000, 50)

Since this prob is less than 0.5 only minimum amount to be bet i.e. 1 dollar
If sum of coins <5100, then Z = 
P(Z<2) = 0.9500
This time we can bet maximum of 100 dollars as probability is very high nearer to 1.
Answer:
326,000
Step-by-step explanation:
326,000 is the answer.