Question

12x⁴ + 30x³ + 4x² + 10x
Ax(Bx² + 1) (2x + 5)
B=[___________]

Answer 1

To simplify the given expression, use the distributive property and simplify each term within the parentheses. Multiply the terms inside the parentheses with the term outside the parentheses.

Step-by-step explanation:

The given expression is: 12x⁴ + 30x³ + 4x² + 10xAx(Bx² + 1) (2x + 5). To simplify this expression, use the distributive property and simplify each term within the parentheses. Start by multiplying the terms inside the parentheses with the term outside the parentheses, and then combine like terms to simplify the expression.

A step-by-step simplification of the given expression is:

1. Multiply 10xAx by 2x to get 20x²Ax² + 10xAx, and multiply it by Bx² + 1 to get 20x²Ax²Bx² + 20x²Ax²
2. Multiply 10xAx by 5 to get 50xAx and multiply it by Bx² + 1 to get 50xAxBx² + 50xAx
3. Add all the obtained terms: 12x⁴ + 30x³ + 4x² + 20x²Ax²Bx² + 20x²Ax² + 50xAxBx² + 50xAx
4. Combine like terms: 12x⁴ + 30x³ + (20x²Ax²Bx² + 20x²Ax²) + (50xAxBx² + 50xAx)

There is no further simplification possible, so the simplified expression is 12x⁴ + 30x³ + 20x²Ax²Bx² + 20x²Ax² + 50xAxBx² + 50xAx.