Answer :
We begin with the expression
$$
2x^3(5x^3 - 7).
$$
Step 1: Distribute \( 2x^3 \) across the terms inside the parentheses. This gives:
$$
2x^3(5x^3) - 2x^3(7).
$$
Step 2: Multiply the coefficients and add the exponents of like bases for the first term:
$$
2 \cdot 5 = 10,
$$
and since
$$
x^3 \cdot x^3 = x^{3+3} = x^6,
$$
the first term becomes:
$$
10x^6.
$$
Step 3: Multiply the second term:
$$
2x^3 \cdot 7 = 14x^3,
$$
and since it is subtracted, the second term is:
$$
-14x^3.
$$
Step 4: Putting it all together, the simplified expression is:
$$
10x^6 - 14x^3.
$$
So, the correct answer is:
$$
\boxed{10x^6 - 14x^3}.
$$
$$
2x^3(5x^3 - 7).
$$
Step 1: Distribute \( 2x^3 \) across the terms inside the parentheses. This gives:
$$
2x^3(5x^3) - 2x^3(7).
$$
Step 2: Multiply the coefficients and add the exponents of like bases for the first term:
$$
2 \cdot 5 = 10,
$$
and since
$$
x^3 \cdot x^3 = x^{3+3} = x^6,
$$
the first term becomes:
$$
10x^6.
$$
Step 3: Multiply the second term:
$$
2x^3 \cdot 7 = 14x^3,
$$
and since it is subtracted, the second term is:
$$
-14x^3.
$$
Step 4: Putting it all together, the simplified expression is:
$$
10x^6 - 14x^3.
$$
So, the correct answer is:
$$
\boxed{10x^6 - 14x^3}.
$$
