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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
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Multiply the first terms: (7b^5) * (7b^5) = 49b^10
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Multiply the outer terms: (7b^5) * (-b^2) = -7b^7
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Multiply the inner terms: (-b^2) * (7b^5) = -7b^7
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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.