A coefficient can multiply one or more variables raised to powers {term, algebra}. Terms can add.
simplification
To simplify terms with parentheses, first remove exponents outside parentheses by multiplying exponent by all term exponents, including exponents of 1. After removing parentheses, multiply term factors. Make term have fewest variables and coefficients.
If term has more than one constant or repeats same variable, first multiply coefficients, including signs, to obtain one coefficient. Then, for all variables, add exponents.
addition
To add or subtract terms, first put terms in simplest form. Then add coefficients of terms that have same variables with same exponents.
unknowns {cosa}.
Terms {similar term} {like term} can differ only in numerical or literal coefficient.
Expressions can have irrational numbers {surd}. Expressions {pure surd} can have irrational numbers in all terms. Expressions {entire surd} can have no rational factors.
Numbers {coefficient} {constant, algebra}, or letters that equal constants, can multiply variables. Coefficients have no exponent.
Coefficients {literal coefficient} can use letters, instead of numbers.
Letters {variable, algebra} can have values. Variables can have constant or variable exponents.
Variables {base, exponent} can have exponents {exponent, variable} {power, variable}. To multiply variable with exponent with same variable with exponent, add exponents: x^3 * x^2 = x^5. To divide variable with exponent by same variable with exponent, subtract exponents: x^3 / x^2 = x^1. To raise variable with exponent to power, multiply exponent and power: (e^x)^3 = e^(3*x).
Expressions {monomial} can have one term.
Sums can have two terms {binomial}.
Sums can have three terms {trinomial}.
Sums can have more than one term {polynomial}.
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Date Modified: 2022.0225