Final answer:
To simplify the expression 2x³(5x⁴ - 7x² + 2), distribute 2x³ across each term inside the parentheses to obtain 10x⁷ - 14x⁵ + 4x³. Eliminate any like terms if possible and check the result for correctness.
Step-by-step explanation:
To find the product and simplify the expression 2x³(5x⁴ - 7x² + 2), you should apply the distributive property of multiplication over addition. This involves multiplying each term inside the parentheses by 2x³.
- Multiply 2x³ by 5x⁴ to get 10x⁷.
- Multiply 2x³ by -7x² to get -14x⁵.
- Multiply 2x³ by 2 to get 4x³.
After performing these steps, the simplified expression is 10x⁷ - 14x⁵ + 4x³.
To ensure this process is correct, one can eliminate terms wherever possible and check the answer to see if it is reasonable.