Expanding the Square: (7b^5  b^2)^2
In mathematics, expanding a squared expression means multiplying it by itself. Let's break down the steps to expand (7b^5  b^2)^2.
Understanding the Concept
The expression (7b^5  b^2)^2 is equivalent to:
(7b^5  b^2) * (7b^5  b^2)
We need to apply the distributive property (or FOIL method) to multiply each term in the first set of parentheses by each term in the second set.
Expanding the Expression

Multiply the first terms: (7b^5) * (7b^5) = 49b^10

Multiply the outer terms: (7b^5) * (b^2) = 7b^7

Multiply the inner terms: (b^2) * (7b^5) = 7b^7

Multiply the last terms: (b^2) * (b^2) = b^4
Combining Like Terms
Now, we combine the terms we obtained:
49b^10  7b^7  7b^7 + b^4
Finally, we simplify by combining the like terms:
49b^10  14b^7 + b^4
Final Result
Therefore, the expanded form of (7b^5  b^2)^2 is 49b^10  14b^7 + b^4.