Final answer:
The distributive property of multiplication over addition, A(B + C) = AB + AC, allows multiplication to be 'distributed' over terms being added or subtracted. This property is also utilized in vector mathematics for dot and cross product operations.
Step-by-step explanation:
The distributive property of multiplication over addition can be simply stated as A(B + C) = AB + AC. This implies that when you multiply a number by a sum, you can multiply each addend separately and then add the results. This property also applies to multiplication over subtraction, as in A(B - C) = AB - AC.
When dealing with multiplication or division by a number, these operations should apply to every term in an equation. According to the rules of multiplication, when two positive numbers or two negative numbers are multiplied together, the answer has a positive sign, while multiplying numbers with opposite signs gives an answer with a negative sign.
Additionally, vector mathematics utilizes the distributive property as well. When vectors are added together and multiplied by scalars, operations follow the distributive property. For example, when determining the dot product or the cross product of vectors expressed in components, the distributive property is frequently applied.
This allows for operations to be performed scalar by scalar and vector by vector, yielding a simplified and calculated result. Understanding the distributive property helps in solving equations and manipulating algebraic expressions efficiently.
The complete question is: okay so I need to put distributive property of multiplication over addition, multiplication, and addition can someone tell me the answer's is: