-18x^5-204x^4-722x^3-600x^2+672x-128
[tex]( - 18 {x}^{2} + 12x - 2)[/tex]
[tex]( {x}^{3} + 12 {x}^{2} + 48x + 64)[/tex]
There are multiple ways to solve this for example the foil method or the box method. I prefer to do the box method.
First we are going to set it up
After we set it up we have to solve it so first we are going to multiply
[tex] {x}^{3} \times - 18 {x}^{2} = - 18 {x}^{5} [/tex]
We have to add the exponent
[tex] - 18 {x}^{2} \times 12 {x}^{2} = - 216 {x}^{4} [/tex]
[tex] - 18 {x}^{2} \times 48x = - 864 {x}^{3 } \\ - 18{x}^{2} \times 64 = - 1152 {x}^{2} \\ 12x \times {x}^{3} = 12 {x}^{4} \\ 12x \times 12 {x}^{2} = 144 {x}^{3} [/tex]
[tex]12x \times 48x = 576 {x}^{2} \\ 12x \times 64 = 768x [/tex]
[tex] - 2 \times {x}^{3} = - 2 {x}^{3} \\ - 2 \times 12 {x}^{2} = - 24 {x}^{2} \\ - 2 \times 48x = - 96x \\ - 2 \times 64 = - 128[/tex]
Now we have to add them
-18x^5 stays because there is nothing to add to
Now we add the rest
[tex] -216 {x}^{4} + 12 {x}^{4} = - 204 {x}^{4} [/tex]
[tex] - 864 {x}^{3} + 144 {x}^{3} + - 2 {x}^{3} = - 722 {x}^{3} [/tex]
[tex]768x - 96x = 672x[/tex]
And -128 stays the same
[tex] - 1152 {x}^{2} + 576 {x}^{2} - 24 {x}^{2} = - 600 {x}^{2} [/tex]
The answer is
-18x^5-204x^4-722x^3-600x^2+672x-128
