Question

What is the product of these polynomials
`(6 {x}^(2) - 3x - 6)(4 {x}^(2) + 5x + 4)`

Answer 1

The given expression is:

`(6x^2-3x-6)(4x^2+5x+4)`

Distribute the second polynomial into the first:

`6x^2(4x^2+5x+4)-3x(4x^2+5x+4)-6(4x^2+5x+4)`

Multiply the expressions:

`24x^4+30x^3+24x^2-12x^3-15x^2-12x-24x^2-30x-24`

Simplify the expression:

`\begin{gathered} 24x^4+30x^3-12x^3+24x^2-15x^2-24x^2-12x-30x-24 \\ =24x^4+18x^3-15x^2-42x-24 \end{gathered}`

The answer is:

`24x^4+18x^3−15x^2−42x−24`