Final answer:
To simplify the expression 3x²(7x² + 2x − 4), we distribute 3x² across each term inside the parentheses, resulting in the expression 21x⁴ + 6x³ − 12x².
Step-by-step explanation:
The question asks us to simplify the algebraic expression: 3x²(7x² + 2x − 4). To do this, we will use the distributive property to multiply 3x² by each term inside the parentheses.
- Multiply 3x² by 7x², which gives us 21x⁴ (because x² times x² is x⁴).
- Multiply 3x² by 2x, which gives us 6x³.
- Multiply 3x² by -4, which gives us -12x².
Combining all the terms, we get the simplified expression: 21x⁴ + 6x³ − 12x².