Final answer:
The expression (10x+3y)² expands to 100x² + 60xy + 9y² by using the binomial square formula. This involves algebraic manipulation, and a similar concept applies to multiplying powers of 10 or using scientific notation.
Step-by-step explanation:
The question asks about expanding a binomial expression and employs concepts from algebra, specifically the use of binomial squares. To expand (10x+3y)², we apply the formula (a+b)² = a² + 2ab + b². Using this, we get:
(10x+3y)² = (10x)² + 2*(10x)*(3y) + (3y)² = 100x² + 60xy + 9y².
This expression simplifies to 100x² + 60xy + 9y². It's important to note that in algebra, understanding how to manipulate exponents and binomials is crucial. For example, when multiplying powers of 10, such as in the expression 10² × 10³, the exponents are added to obtain 10⁵ (10 to the power of 5). Similarly, with scientific notation, numbers can be written more compactly, as seen with numbers like 1.372568 × 10⁶, which indicates a large number written with an exponent.