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Title: Intermediate Algebra: Multiplication of polynomials using FOIL method
Description: The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outer, Inner, Last, which describes the order in which you multiply the terms. For example, when multiplying \((a + b)(c + d)\), you multiply the First terms (\(a \cdot c\)), the Outer terms (\(a \cdot d\)), the Inner terms (\(b \cdot c\)), and the Last terms (\(b \cdot d\)). Finally, you combine like terms to simplify the expression. This method effectively demonstrates how to delve into polynomial multiplication in a structured way.
Description: The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outer, Inner, Last, which describes the order in which you multiply the terms. For example, when multiplying \((a + b)(c + d)\), you multiply the First terms (\(a \cdot c\)), the Outer terms (\(a \cdot d\)), the Inner terms (\(b \cdot c\)), and the Last terms (\(b \cdot d\)). Finally, you combine like terms to simplify the expression. This method effectively demonstrates how to delve into polynomial multiplication in a structured way.
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Special Products and Factors
In mathematics, polynomials, especially in the form of factors, of p
...
It is generally long and tedious to follow tedious procedures for
obtaining these products and factors by brute-multiplying and dividing
...
One
method is the use of formulas, where a product and factor may be found simply by being
familiar with certain forms and combinations
...
Before discussing the special cases, we
first want to review the original process of obtaining products of polynomials
...
Multiplication of Polynomials
Note!
- When we multiply a polynomial by a monomial, both the distributive property and the
laws of exponents are applied
...
a
...
-4x2y(9x2 – 2xy + 5y2)
Solution:
a
...
-4x2y(9x2 – 2xy + 5y2) = -36x4y + 8x3y2 – 20x2y3
Note!
- Multiply every term of the polynomial by the monomial
...
Example #2
Multiply (5x – 3)(x + 4)
...
FOIL is an
acronym meaning we sum the product of the First terms, Outer terms, Inner terms, and
Last terms
...
a
...
(5x – 9y)(4x – 3y)
Solution:
a
...
Thus, (x + 3)(5x – 2) = 15x2 – 2x + 15x – 6
15x2 + 13x = 6
b
Title: Intermediate Algebra: Multiplication of polynomials using FOIL method
Description: The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outer, Inner, Last, which describes the order in which you multiply the terms. For example, when multiplying \((a + b)(c + d)\), you multiply the First terms (\(a \cdot c\)), the Outer terms (\(a \cdot d\)), the Inner terms (\(b \cdot c\)), and the Last terms (\(b \cdot d\)). Finally, you combine like terms to simplify the expression. This method effectively demonstrates how to delve into polynomial multiplication in a structured way.
Description: The FOIL method is a technique used to multiply two binomials. FOIL stands for First, Outer, Inner, Last, which describes the order in which you multiply the terms. For example, when multiplying \((a + b)(c + d)\), you multiply the First terms (\(a \cdot c\)), the Outer terms (\(a \cdot d\)), the Inner terms (\(b \cdot c\)), and the Last terms (\(b \cdot d\)). Finally, you combine like terms to simplify the expression. This method effectively demonstrates how to delve into polynomial multiplication in a structured way.