Distributive Property: x(3x^2 - 5x + 8)

Question

x(3x^2 - 5x + 8)

Answer 1

When you distribute a constant, you multiply it. Here, it's to each value within the parentheses. So:

x(3x² - 5x +8) =  3x²(x) - 5x(x) + 8(x)

When multiplying unknown variables (like 'x'), the product is that variable raised to the sum (addition) of their power.

For example: x³(x²) = x³⁺² = x⁵  ,  or: y⁵(y⁴) = y⁵⁺⁴ = y⁹

Also, a variable with 'no exponent' actually has an exponent of 1. So, x = x¹.

For example: x³(x) = x³⁺¹ = x⁴

To finish your question,

3x²(x) - 5x(x) + 8(x) = 3x²⁺¹ - 5x¹⁺¹ + 8x = 3x³ - 5x² + 8x