Final answer:
The expression (5x² + 3x - 4) × (5x² + 5x - 1) needs to be expanded using the FOIL method. After multiplying and combining like terms, we obtain a polynomial. However, the provided answer options do not match the correct expansion of the expression.
Step-by-step explanation:
To simplify the expression (5x² + 3x - 4) × (5x² + 5x - 1), we need to apply the FOIL method (First, Outer, Inner, Last), which is a way of expanding expressions that are products of two binomials.
The steps to solve this are:
- Multiply the First terms: (5x²) × (5x²) = 25x⁴
- Multiply the Outer terms: (5x²) × (5x) = 25x³
- Multiply the Inner terms: (3x) × (5x²) = 15x³
- Multiply the Last terms: (3x) × (5x) = 15x²
- Continue by multiplying each term in the first parenthesis by each term in the second parenthesis.
- Combine like terms.
After completing these steps, we will arrive at a polynomial. However, since none of the provided answer options (a, b, c, d) correctly reflect the result of expanding the given expression, it seems there may be a mistake in the question or the answer choices.