What is the coefficient of x^3 when
24x^4+6x^3+4x^2-7x-5
is multiplied by
6x^3+3x^2+3x+4
and the like terms are combined?
+4622 As you can see, just distribute as these range by increasing power. The answer should be -15. \(144x^7+108x^6+114x^5+84x^4\boxed{-15}x^3-20x^2-43x-20\)
+1252 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
