Use the distributive property to calculate each value mentally. 72*17+28*17

Verified step by step guidance

1. Recognize that the expression $72\times 17+28\times 17$ can be simplified using the distributive property.
2. Factor out the common factor of 17 from both terms: $17\times (72+28)$.
3. Calculate the sum inside the parentheses: $72+28$.
4. Multiply the result of the sum by 17: $17\times (\text{sum})$.
5. This approach allows you to calculate the expression mentally by simplifying the multiplication process.

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside a set of parentheses. In the context of the given question, it can be applied to factor out the common term (17) from both products, simplifying the calculation.

Mental Math Techniques

Mental math techniques involve strategies that enable individuals to perform calculations in their heads without the use of paper or calculators. Techniques such as breaking numbers into smaller, more manageable parts or using the distributive property can significantly speed up calculations and improve accuracy.

Factoring

Factoring is the process of breaking down an expression into simpler components, often to simplify calculations. In this problem, recognizing that both terms (72*17 and 28*17) share a common factor (17) allows us to rewrite the expression as 17*(72 + 28), making it easier to compute the final result.