Question

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

Answer 1

`y=12x^2+25x+12`

Explanation:

To rewrite the equation in standard form, expand the brackets.

`y=(color(red)(4x)` `color(green)(+3))(color(orange)(3x)` `color(blue)(+4))`

`y=color(red)(4x)(color(orange)(3x))` `color(red)(+4x)(color(blue)(4))` `color(green)(+3)(color(orange)(3x))` `color(green)(+3)(color(blue)(4))`

Simplify.

`y=12x^2+16x+9x+12`

`y=12x^2+25x+12`

Answer 2

`color(blue)("A slightly different way of thinking about the method.")`

`12x^2+25x+12`

Explanation:

Given: `color(blue)((4x+3)color(red)((3x+4))`

Using the Distributive property

`color(blue)(4xcolor(red)((3x+4))+3color(red)((3x+4)))`

`(12x^2 +16x) +(9x+12)`

As there is no multiplication left to do we can 'get rid' of the brackets

`12x^2 +16x +9x+12`

`12x^2+25x+12`