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- https://math.libretexts.org/Courses/Nova_Scotia_Community_College/MATH_1043/02%3A_Algebra/2.02%3A_The_Fundamentals_of_Algebra/2.2.04%3A_Simplifying_Algebraic_ExpressionsThe commutative property allows us to change the order of multiplication without affecting the product or answer. The associative property allows us to regroup without affecting the product or answer.
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/06%3A_The_Fundamentals_of_Algebra/6.03%3A_Simplifying_Algebraic_Expressions\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -1...\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -15y.} \\ = - 18t - 63 ~ & \textcolor{red}{ \text{ Write the answer in simpler form.}} \\ ~ & \textcolor{red}{ \text{ Subtracting } -15y \text{ is the same as adding } 15y.} \end{aligned}\nonumber \]
- https://math.libretexts.org/Under_Construction/Stalled_Project_(Not_under_Active_Development)/Book%3A_Beginning_Algebra_(Feiner)/2%3A_The_Commutative%2C_Associative%2C_and_Distributive_Laws%2F%2FProperties/2.2%3A_The_Commutative_Property_of_Addition_and_MultiplicationIf we find one counterexample, one example that shows that subtraction is not commutative, the general property (using \(a\) and \(b\)) does not exist. where \(a\) and \(b\) are any real numbers (like...If we find one counterexample, one example that shows that subtraction is not commutative, the general property (using \(a\) and \(b\)) does not exist. where \(a\) and \(b\) are any real numbers (like \(-6.4\), \(\displaystyle \frac{2}{7}\), \(\pi\)). Any real number can hide in the \(a\)-box or the \(b\)-box. If we find one counterexample, one example that shows that division is not commutative, the general property (using \(a\) and \(b\)) does not exist
- https://math.libretexts.org/Courses/Las_Positas_College/Foundational_Mathematics/02%3A_Integers/2.13%3A_Simplifying_(Still_Not_Solving)_Algebraic_Expressions)/2.13.01%3A_Simplifying_Algebraic_Expressions\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -1...\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -15y.} \\ = - 18t - 63 ~ & \textcolor{red}{ \text{ Write the answer in simpler form.}} \\ ~ & \textcolor{red}{ \text{ Subtracting } -15y \text{ is the same as adding } 15y.} \end{aligned}\nonumber \]
- https://math.libretexts.org/Courses/Santiago_Canyon_College/HiSet_Mathematica_(Lopez)/05%3A_Multiplicacion_y_division_de_numeros_enteros/5.05%3A_Propiedades_de_la_MultiplicacionSi se multiplican tres números enteros, el producto será el mismo si los dos primeros se multiplican primero y luego ese producto se multiplica por el tercero, o si los dos segundos se multiplican pri...Si se multiplican tres números enteros, el producto será el mismo si los dos primeros se multiplican primero y luego ese producto se multiplica por el tercero, o si los dos segundos se multiplican primero y ese producto se multiplica por el primero. El hecho de que\(1 \cdot \text{ any number} = \text{that particular number}\) sea un ejemplo de la propiedad de la multiplicación.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/1%3A_Simplifying_Expressions/1.02%3A_FOIL_Method_and_Special_ProductsIn this section, examples are given for multiplying a binomial (2-term polynomial) to another binomial. In some cases, the FOIL method yields predictable patterns. We call these “special products.” Re...In this section, examples are given for multiplying a binomial (2-term polynomial) to another binomial. In some cases, the FOIL method yields predictable patterns. We call these “special products.” Recognizing special products will be useful when we turn to solving quadratic equations
- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_PreAlgebra/01%3A_Whole_Numbers/1.03%3A_Multiplying_and_Dividing_Whole_NumbersWe begin this section by discussing multiplication of whole numbers. The first order of business is to introduce the various symbols used to indicate multiplication of two whole numbers.
- https://math.libretexts.org/Courses/Barton_Community_College/Book%3A_Technical_Mathematics_(Turner)/07%3A_The_Integers/7.04%3A_Multiplication_and_Division_of_IntegersIntegers satisfy the same properties of multiplication as do the whole numbers.
- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_PreAlgebra/04%3A_Introduction_to_Algebra/4.03%3A_Simplifying_Algebraic_ExpressionsThe commutative property allows us to change the order of multiplication without affecting the product or answer. The associative property allows us to regroup without affecting the product or answer.
- https://math.libretexts.org/Courses/Honolulu_Community_College/Math_75X%3A_Introduction_to_Mathematical_Reasoning_(Kearns)/04%3A_Fundamentals_of_Algebra/4.04%3A_Simplifying_(Still_Not_Solving)_Algebraic_Expressions)/4.4.00%3A_Simplifying_Algebraic_Expressions\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -1...\[ \begin{aligned} -5(4-3y) = -5(4)-(-5)(3y) ~ & \textcolor{red}{ \text{ Distribute multiplication by }-5.} \\ = -20-(-15y) ~ & \textcolor{red}{ \text{ Multiply: } -5(4) = -20 \text{ and } -5(3y) = -15y.} \\ = - 18t - 63 ~ & \textcolor{red}{ \text{ Write the answer in simpler form.}} \\ ~ & \textcolor{red}{ \text{ Subtracting } -15y \text{ is the same as adding } 15y.} \end{aligned}\nonumber \]
- https://math.libretexts.org/Courses/Nova_Scotia_Community_College/MATH_1043/02%3A_Algebra/2.01%3A_The_Integers/2.1.04%3A_Multiplication_and_Division_of_IntegersIntegers satisfy the same properties of multiplication as do the whole numbers.
