代数表达式与恒等式

Introduction: From Numbers to Algebra

Real Variables, Monomials, and Polynomials

Which of the following statements is correct?

Algebraic Identities

Which of the following is an identity (holds for all real values)?

Deriving Identities (a)(b) with Distributivity

After expanding $(x+4)^2$, what is the middle (cross) term?

Sum and Difference of Cubes Formulas

After expanding $(x+2)^3$, how many terms are there?

Worked Example: Expanding the Cube of a Sum

Use the difference-of-squares formula to compute $101^2-99^2$. Enter an integer.

Use the difference-of-squares formula to factor $x^2-25$ as the product of two linear factors (no spaces).

A student expanded $(2x+3)^2$ as $4x^2+9$. Which term was omitted? Write the missing term (with coefficient and variable, no spaces).

What does $(x+y)^2$ expand to?

Explain in your own words: what is the fundamental difference between an algebraic identity and an equation? Give one example of each.

Comprehensive Check

Correcting Common Errors and Lesson Summary