Distributive Property of Multiplication over Addition in Algebra
A student can apply the rule \( a(b + c) = ab + ac \) to expand a single factor across every term inside a grouping, for numeric factors, variable factors, and mixed expressions, and can extend it to any number of terms and to subtraction by treating subtraction as adding a negative. They can also run it in reverse, pulling a common factor out of every term. They know the boundary: the property distributes over terms joined by addition or subtraction, never over members joined by multiplication or division.
The Distributive Property of Multiplication over Addition in Pre-Algebra
The distributive property of multiplication over addition states that for any numbers a, b, and c, a × (b + c) = (a × b) + (a × c): multiplying a sum by a factor is equivalent to multiplying each add…