-5x^6(3x^2 - 12x +30)

Answer 1

To simplify the expression $-5x^6(3x^2-12x+30)$, you need to distribute $-5x^6$ to each term inside the parentheses:

1. Multiply $-5x^6$ by $3x^2$: $$-5x^6\cdot 3x^2=-15x^{6+2}=-15x^8$$

2. Multiply $-5x^6$ by $-12x$: $$-5x^6\cdot (-12x)=60x^{6+1}=60x^7$$

3. Multiply $-5x^6$ by $30$: $$-5x^6\cdot 30=-150x^6$$

Now, combine all the results together: $$-15x^8+60x^7-150x^6$$

Thus, the simplified expression is: $$-15x^8+60x^7-150x^6$$