Expanding the Square of a Binomial
In mathematics, we often encounter expressions that require us to expand squares of binomials. One such expression is (7b^5  b^2)^2. Let's explore how to expand this expression and understand the underlying principles involved.
Understanding the Concept
The expression (7b^5  b^2)^2 represents the square of the binomial (7b^5  b^2). In simpler terms, it means multiplying the binomial by itself:
(7b^5  b^2)^2 = (7b^5  b^2) * (7b^5  b^2)
Applying the FOIL Method
To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last. This method helps us systematically multiply each term in the first binomial by each term in the second binomial.

First: Multiply the first terms of each binomial:
(7b^5) * (7b^5) = 49b^10 
Outer: Multiply the outer terms of the binomials: (7b^5) * (b^2) = 7b^7

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

Last: Multiply the last terms of the binomials: (b^2) * (b^2) = b^4
Combining Like Terms
Now, we have the following terms:
49b^10  7b^7  7b^7 + b^4
Combining the like terms (7b^7 and 7b^7), we get:
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.
This process demonstrates how to expand the square of a binomial by applying the FOIL method and combining like terms.