Question

2(x+7)+4x распределительный закон умножения

Answer 1

2(x+7)+4x= 2х+14+4х=6х+14

Answer 2

Distributive Law of Multiplication

The distributive law of multiplication states that for any numbers a, b, and c, the following equation holds true: a * (b + c) = a * b + a * c. This law allows us to distribute the multiplication over addition or subtraction.

For example, if we have the expression 2(x + 7), we can apply the distributive law of multiplication to expand it as follows: 2(x + 7) = 2 * x + 2 * 7 = 2x + 14.

This law is a fundamental property of arithmetic and is widely used in algebraic manipulations.

Additional Examples and Applications

The distributive law of multiplication can be applied to various algebraic expressions. For instance, consider the expression x^2 - 5x + 7. We can use the distributive law to factor out common terms: x^2 - 5x + 7 = (x^2 - 5x) + 7 = x(x - 5) + 7.

Another example involves the expression 4x^2 - 4y - x^2 + 17y - y: 4x^2 - 4y - x^2 + 17y - y = (4x^2 - x^2) + (-4y + 17y - y) = 3x^2 + 12y.

These examples illustrate the application of the distributive law of multiplication in simplifying algebraic expressions by factoring out common terms.

Conclusion

The distributive law of multiplication is a fundamental concept in mathematics, particularly in algebra. It allows for the expansion and simplification of expressions by distributing the multiplication over addition or subtraction. This law plays a crucial role in various algebraic manipulations and is essential for understanding and solving mathematical problems.

If you have further questions or need more examples, feel free to ask!