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Taught fractal geometry, calculus, algebra, analysis and elementary number theory before. Comfortable with most areas of pure maths. Finished my MMath degree at the university of St Andrews. LinkedIn: https://www.linkedin.com/in/anastasios-stylianou-8b921287/Warwick: https://warwick.ac.uk/fac/sci/maths/people/staff/stylianou

We can find the coefficients in the expansion of$(a+b)^{n}$ from the nth row of __________ triangle. So $(a+b)^{4}=\square a^{4}+\square a^{3} b+\square a^{2} b^{2}+\square a b^{3}+\square b^{4}$

The binomial coefficients can be calculated directly by using the formula $\left(\begin{array}{l}{n} \\ {k}\end{array}\right)$= ___________. So$\left(\begin{array}{l}{4} \\ {3}\end{array}\right)$= _____________.

Perform each indicated operation. Simplify if possible. See Examples I through 7.$$\frac{-8}{x^{2}-1}-\frac{7}{1-x^{2}}$$

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1.$$\log _{5} 2+\log _{5} 7$$

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1.$$\log _{4} 9+\log _{4} x$$

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1.$$\log _{6} x+\log _{6}(x+1)$$