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Expanding the Expression: (2x³ + 1)(5x³ + 4)
This article will guide you through the process of expanding the given expression: (2x³ + 1)(5x³ + 4).
Understanding the Process
The expression represents the product of two binomials. To expand it, we can use the FOIL method, which stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Applying FOIL
Let's apply the FOIL method to our expression:
1. First: (2x³) * (5x³) = 10x⁶
2. Outer: (2x³) * (4) = 8x³
3. Inner: (1) * (5x³) = 5x³
4. Last: (1) * (4) = 4
Combining the Terms
Now, we combine the terms we obtained from the FOIL method:
10x⁶ + 8x³ + 5x³ + 4
Simplifying the Expression
Finally, we simplify the expression by combining like terms:
10x⁶ + 13x³ + 4
Conclusion
Therefore, the expanded form of the expression (2x³ + 1)(5x³ + 4) is 10x⁶ + 13x³ + 4.