(7b5−b2)2

Jasonbradley

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Jun 16, 2024

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Expanding (7b^5 - b^2)^2

The expression (7b^5 - b^2)^2 represents the square of a binomial. To expand this, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

• 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 each binomial: (-b^2)(-b^2) = b^4

Now, combine the terms:

49b^10 - 7b^7 - 7b^7 + b^4 = 49b^10 - 14b^7 + b^4

Using the Square of a Binomial Formula

The square of a binomial formula states: (a - b)^2 = a^2 - 2ab + b^2

In our case, a = 7b^5 and b = b^2. Applying the formula:

(7b^5 - b^2)^2 = (7b^5)^2 - 2(7b^5)(b^2) + (b^2)^2

Simplifying:

(7b^5)^2 - 2(7b^5)(b^2) + (b^2)^2 = 49b^10 - 14b^7 + b^4

Therefore, the expanded form of (7b^5 - b^2)^2 is 49b^10 - 14b^7 + b^4.