The distributive property is a fundamental principle in algebra that describes how to multiply a single term by a sum or difference within parentheses. According to the distributive property, when you have an expression like \( a(b + c) \) or \( a(b - c) \), you can distribute the multiplication across the terms inside the parentheses.
Mathematically, it is expressed as:
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For addition:
\[ a(b + c) = ab + ac \] -
For subtraction:
\[ a(b - c) = ab - ac \]
In these formulas, \( a \), \( b \), and \( c \) can be any numbers or algebraic expressions. This property is useful for simplifying expressions and solving equations.
For example, if you want to simplify \( 3(2 + 4) \), you can use the distributive property:
\[ 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 = 6 + 12 = 18 \]
Or you can simply calculate \( 3(6) \) directly, which also gives \( 18 \).
Using the distributive property can help reduce computation steps and clarify expressions in algebra.
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