2.jpeg "(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.