Question

Find the product of -3x^3+2x-4 and x^3+x-2​

Answer 1

`-3x^6-x^4+2x^3+2x^2-8x+8`

Explanation:

we have

`(-3x^(3)+2x-4)(x^(3)+x-2)`

Applying distributive property

`(-3x^3)(x^3)+(-3x^3)(x)+(-3x^3)(-2)+(2x)(x^3)+(2x)(x)+(2x)(-2)+(-4)(x^3)+(-4)(x)+(-4)(-2)`

Remember the properties

`(-1)(-1)=(+1)\\(-1)(+1)=(-1)`

`x^(m)x^(n)=x^(m+n)`

so

`(-3x^6)+(-3x^4)+(6x^3)+(2x^4)+(2x^2)+(-4x)+(-4x^3)+(-4x)+(8)`

Combine like terms

`-3x^6-x^4+2x^3+2x^2-8x+8`