Factors; coefficient; exponent; power; base; term; algebraic sum; similar terms; degree; homogeneous expression; linear equation; root of an equation; root of an expression; identity; conditional equation; prime quantity; highest common factor (H. C. F.); lowest common multiple (L. C. M.); involution; evolution; imaginary number; real number; rational; similar radicals; binomial surd; pure quadratic equation; affected quadratic equation; equation in the quadratic form; simultaneous linear equations; simultaneous quadratic equations; discriminant; symmetrical expression; ratio; proportion; fourth proportional; third proportional; mean proportional; arithmetic progression; geometric progression;

1. Square of the sum of two quantities.

2. Square of the difference of two quantities.

3. Product of the sum and difference of two quantities.

4. Product of two binomials having a common term.

5. Product of two binomials whose corresponding terms are similar.

6. Square of a polynomial.

7. Sum of two cubes.

8. Difference of two cubes.

9. Sum or difference of two like powers.

1. Common monomial factor.

2. Trinomial that is a perfect square.

3. The difference of two squares.

4. Trinomial of the form

5. Trinomial of the form

6. Sum or difference of

• two cubes. See "Special Rules," 7 and 8.
• two like powers. See "Special Rules," 9.

7. Common polynomial factor. Grouping.

8. Factor Theorem.

H. C. F.

L. C. M.

Reduction to lowest terms.

Reduction of a mixed number to an improper fraction.

Reduction of an improper fraction to a mixed number.

Addition