Basic Mathematics Fundamentals

To combine like terms only when variables share exponents

To expand products across sums, like a(b + c) = ab + ac

To reverse the order of operations between addition and multiplication

Its slope changes depending on x

It always passes through the origin

It is a straight line with constant rate of change

Estimate graphically only, since exact methods are unnecessary

Always apply matrix inversion regardless of simplicity

Use substitution or elimination depending on coefficients

Flip the second fraction and multiply numerators only

Add numerators and denominators separately

Multiply numerators and multiply denominators, then simplify

All odd numbers greater than one are prime

A prime has exactly two distinct positive divisors: 1 and itself

Primes can be composed by multiplying smaller primes

They cannot occur at the same time

Their probabilities must both equal one half

The occurrence of one doesn't change the probability of the other

Compare with a numerical difference quotient for small increments

Differentiate twice and ensure the result is zero

Integrate the original function and compare

To change a linear equation into exponential form

To solve quadratics and rewrite them as a perfect square plus constant

To multiply polynomials faster

It converges when the common ratio has absolute value less than one

It converges only when the first term is less than one

It converges if the ratio is any positive number

To estimate values using derivatives when exact evaluation is hard

To guarantee exact equality at distant points

To transform any function into a polynomial globally