Question

How do you find the product `(x^2-4x+5)(5x^2+3x-4)`?

Answer 1

`5x^4-17x^3+9x^2+31x-20`

Explanation:

`"each term in the second factor is multiplied by each term"`
`"in the first factor"`

`rArr(color(red)(x^2-4x+5))(5x^2+3x-4)`

`=color(red)(x^2)(5x^2+3x-4)color(red)(-4x)(5x^2+3x-4)`
`color(white)(=)color(red)(+5)(5x^2+3x-4)`

`"distribute each bracket and collect like terms"`

`=5x^4+3x^3-4x^2-20x^3-12x^2`+16x
`color(white)(=)+25xx^2+15x-20`

`=5x^4-17x^3+9x^2+31x-20`