Final answer:
The equivalent expression for 2x (2^3 x) + 3x (5x^2) - 10x is 15x^3 + 16x^2 - 10x, after applying exponents, multiplication, and combining like terms.
Step-by-step explanation:
The question is asking for an equivalent expression for the algebraic expression 2x × (2^3 × x) + 3x × (5x^2) - 10x. To find the equivalent expression, we need to apply the exponent to the terms inside the parentheses, distribute the multiplication across terms, and combine like terms where possible.
First, we apply the exponent to the terms inside the parentheses, resulting in 2x × (8x) for the first term. This simplifies to 16x^2.
Next, we perform the multiplication in the second term, which is 3x × 5x^2, resulting in 15x^3.
Last, we combine the simplified terms with the last term -10x, which does not require any algebraic operations. Combining the terms, we get 16x^2 + 15x^3 - 10x.
Therefore, the equivalent expression is 15x^3 + 16x^2 - 10x.