The statement \( x(7 + 3) = x \times 7 + x \times 3 \) demonstrates a fundamental property in algebra known as the distributive property of multiplication over addition. To better understand this, let's break it down step by step:
1. Expression Interpretation:
- You start with an expression where a term \( x \) is to be multiplied by a sum, \( (7 + 3) \).
2. Application of the Distributive Property:
- The distributive property of multiplication over addition states that when a single term is multiplied by a sum of two or more terms, you can distribute the multiplication over each term in the sum separately.
- Mathematically, this can be written as:
[tex]\[
x(a + b) = x \times a + x \times b
\][/tex]
3. Applying to the Given Expression:
- Here, \( x = 6 \), \( a = 7 \), and \( b = 3 \).
- According to the distributive property:
[tex]\[
6(7 + 3) = 6 \times 7 + 6 \times 3
\][/tex]
4. Demonstration through Expansion:
- First, expand the expression inside the parentheses by multiplying \( 6 \) by each term in the sum:
[tex]\[
6(7 + 3) = 6 \times 7 + 6 \times 3
\][/tex]
- Here, we multiplied \( 6 \) by \( 7 \) and \( 6 \) by \( 3 \) separately.
5. Conclusion:
- The rewritten form \( 6 \times 7 + 6 \times 3 \) confirms that the distributive property has been applied correctly.
- Hence, the given statement \( 6(7 + 3) = 6 \times 7 + 6 \times 3 \) indeed illustrates the distributive property of multiplication over addition.
In conclusion, the distributive property allows you to multiply each addend separately and then add the products. This property is a key tool in simplifying and solving algebraic expressions.
