(4t3−5)2

2 min read Jun 16, 2024
(4t3−5)2

Expanding (4t^3 - 5)^2

The expression (4t^3 - 5)^2 represents the square of a binomial. To expand this, we can use the following steps:

1. Understanding the concept:

The square of a binomial is simply the product of the binomial with itself. In this case, we need to multiply (4t^3 - 5) by itself:

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

2. Applying the distributive property:

To expand the product, we use the distributive property (also known as FOIL). This means we multiply each term in the first binomial by each term in the second binomial:

(4t^3 - 5)(4t^3 - 5) =

  • (4t^3 * 4t^3) + (4t^3 * -5) + (-5 * 4t^3) + (-5 * -5)

3. Simplifying the expression:

Now we perform the multiplications and combine like terms:

  • 16t^6 - 20t^3 - 20t^3 + 25

Finally, combining the like terms, we get:

16t^6 - 40t^3 + 25

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

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