(4t^3-5)^2=

Jasonbradley

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Jun 16, 2024

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Expanding the Square of a Trinomial: (4t^3 - 5)^2

The expression (4t^3 - 5)^2 represents the square of a binomial. Expanding this requires understanding the concept of squaring a binomial, which can be done using the FOIL method (First, Outer, Inner, Last) or the square of a difference pattern.

1. FOIL Method:

• First: Multiply the first terms of each binomial: (4t^3) * (4t^3) = 16t^6
• Outer: Multiply the outer terms of the binomials: (4t^3) * (-5) = -20t^3
• Inner: Multiply the inner terms of the binomials: (-5) * (4t^3) = -20t^3
• Last: Multiply the last terms of each binomial: (-5) * (-5) = 25

Now, combine the terms:

16t^6 - 20t^3 - 20t^3 + 25

Finally, simplify by combining like terms:

16t^6 - 40t^3 + 25

2. Square of a Difference Pattern:

The square of a difference pattern states that (a - b)^2 = a^2 - 2ab + b^2. In our case, a = 4t^3 and b = 5.

Applying the pattern:

(4t^3)^2 - 2(4t^3)(5) + 5^2

Simplifying:

16t^6 - 40t^3 + 25

Therefore, the expanded form of (4t^3 - 5)^2 is 16t^6 - 40t^3 + 25.