-2.jpeg "(4d 2 −2d 7 ) 2")
Expanding the Expression (4d^2 - 2d^7)^2
This article explores the process of expanding the expression (4d^2 - 2d^7)^2.
Understanding the Concept
The expression (4d^2 - 2d^7)^2 represents the square of a binomial. Squaring a binomial means multiplying it by itself. In this case, we are multiplying:
(4d^2 - 2d^7) * (4d^2 - 2d^7)
Applying the FOIL Method
To expand this, we can use the FOIL method:
- First: Multiply the first terms of each binomial: (4d^2) * (4d^2) = 16d^4
- Outer: Multiply the outer terms of the binomials: (4d^2) * (-2d^7) = -8d^9
- Inner: Multiply the inner terms of the binomials: (-2d^7) * (4d^2) = -8d^9
- Last: Multiply the last terms of each binomial: (-2d^7) * (-2d^7) = 4d^14
Combining Like Terms
Now we have the following expression:
16d^4 - 8d^9 - 8d^9 + 4d^14
Combining the like terms, we get:
4d^14 - 16d^9 + 16d^4
Final Result
Therefore, the expanded form of (4d^2 - 2d^7)^2 is 4d^14 - 16d^9 + 16d^4.