Interpret the structure of expressions. Interpret parts of an expression, such as terms, factors, and coefficients. The “such as” listed are not the only parts of an expression students are expected to know; others include, but are not limited to, degree of a polynomial, leading coefficient, constant term, and the standard form of a polynomial (descending exponents).

Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.

Interpret the structure of expressions. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)ⁿ as the product of P and a factor not depending on P

Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).

Write expressions in equivalent forms to solve problems. Use the properties of exponents to transform expressions for exponential functions. For example the expression (1.15)^t can be rewritten as (1.15 ^1/12)^12t ≈ (1.012)^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.