We want the \(x^3\) coefficient of:
(\(24x^4+6x^3+4x^2-7x-5)(6x^3+3x^2+3x+4)\)
We see that the only ways of this is \(x^3*x^0, x^2*x^1\) .
Therefore, knock out the \(24x^4\) .
Now pair some numbers: \(6x^3\times 4, 4x^2\times 3x, -7x \times 3x^2, -5 \times 6x^3\)
Expanding, we get \(24x^3+12x^3-21x^3-30x^3=3x^3-18x^3=-15x^3\)
Therefore, the coefficient of \(x^3\) is -15.
You are very welcome!
:P
