TABLE OF CONTENTS Expanding polynomials through multiplication is often a step in solving equations. The same is true of polynomial factorization, which, in a sense, is the reverse of polynomial expansion. Polynomial factoring may be simple, as in the case of extracting a common monomial term from each term in a polynomial; or it may be more involved, as when factoring a polynomial into a product of other polynomials. The mathematics of factoring is explained for each of these cases.
Combining expressions through multiplication is called expanding an expression. This process is often needed to clear parentheses; thus it involves the distributive property of multiplication over addition. Exponent rules are applied as needed.
The simplest application of the distributive property of multiplication over addition is that of the monomial by the polynomial. Consider the examples that follow.
Expand the expression 7( ? x + 3 y ? 6).
Solution:
Applying the distributive property to each term in the parentheses gives
Notice that the operation before each term to be multiplied is treated as a sign.
Thus, the number 7 is multiplied by each of the terms, ? x, + 3 y, and ? 6, as shown. Each product is separated by addition. Then the operation and sign are again combined using rules of signed number multiplication to give the final answer.
In this example, no combining of like terms was possible because all of the terms...
