To simplify the expression \(-5x^6(3x^2 - 12x + 30)\), you need to distribute \(-5x^6\) to each term inside the parentheses:
-
Multiply \(-5x^6\) by \(3x^2\): \[ -5x^6 \cdot 3x^2 = -15x^{6+2} = -15x^8 \]
-
Multiply \(-5x^6\) by \(-12x\): \[ -5x^6 \cdot (-12x) = 60x^{6+1} = 60x^7 \]
-
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: \[ -15x^8 + 60x^7 - 150x^6 \]