Question

What is the standard form of `y= (3x-4)(x^2-2x+4)`?

Answer 1

See a solution process below:

Explanation:

We can expand the terms on the right side of the equation by multiplying each term in the parenthesis on the left by each term in the parenthesis on the right:

`y = (color(red)(3x) - color(red)(4))(color(blue)(x^2) - color(blue)(2x) + color(blue)4))` becomes:

`y = (color(red)(3x) xx color(blue)(x^2)) - (color(red)(3x) xx color(blue)(2x)) + (color(red)(3x) xx color(blue)(4)) - (color(red)(4) xx color(blue)(x^2)) + (color(red)(4) xx color(blue)(2x)) - (color(red)(4) xx color(blue)(4))`

`y = 3x^3 - 6x^2 + 12x - 4x^2 + 8x - 16`

We can now group and combine like terms:

`y = 3x^3 - 6x^2 - 4x^2 + 12x + 8x - 16`

`y = 3x^3 + (-6 - 4)x^2 + (12 + 8)x - 16`

`y = 3x^3 + (-10)x^2 + 20x - 16`

`y = 3x^3 - 10x^2 + 20x - 16`