Special Products and Factors
In mathematics, polynomials, especially in the form of factors, of p.1 are found in many
branches of mathematics. It is generally long and tedious to follow tedious procedures for
obtaining these products and factors by brute-multiplying and dividing. Therefore, it would be
more helpful to have a way to find shorter, easier ways to find these products and factors. One
method is the use of formulas, where a product and factor may be found simply by being
familiar with certain forms and combinations. Such products or factors are called special
products, and are only useful in certain special cases. Before discussing the special cases, we
first want to review the original process of obtaining products of polynomials.
A. Multiplication of Polynomials
Note!
- When we multiply a polynomial by a monomial, both the distributive property and the
laws of exponents are applied.
Example #1
Find each product.
a. 2x(5x3 + 3x2 –8x + 4)
b. -4x2y(9x2 – 2xy + 5y2)
Solution:
a. 2x(5x3 + 3x2 –8x + 4) = 10x4 + 6x3 – 16x2 + 8x
In mathematics, polynomials, especially in the form of factors, of p.1 are found in many
branches of mathematics. It is generally long and tedious to follow tedious procedures for
obtaining these products and factors by brute-multiplying and dividing. Therefore, it would be
more helpful to have a way to find shorter, easier ways to find these products and factors. One
method is the use of formulas, where a product and factor may be found simply by being
familiar with certain forms and combinations. Such products or factors are called special
products, and are only useful in certain special cases. Before discussing the special cases, we
first want to review the original process of obtaining products of polynomials.
A. Multiplication of Polynomials
Note!
- When we multiply a polynomial by a monomial, both the distributive property and the
laws of exponents are applied.
Example #1
Find each product.
a. 2x(5x3 + 3x2 –8x + 4)
b. -4x2y(9x2 – 2xy + 5y2)
Solution:
a. 2x(5x3 + 3x2 –8x + 4) = 10x4 + 6x3 – 16x2 + 8x
