Question

What is the standard form of `y= (x+2) (4x+1)`?

Answer 1

`y=4x^2+9x+2`

Explanation:

The "standard form" for a quadratic equation is
`color(white)("XXX")y=ax^2+bx+c`
with constants `a, b, c`

Given `y=(x+2)(4x+1)`
we can convert this into standard form by simply multiplying the two factors on the right side:
`color(white)("XXX")(x+2)(4x+1)=4x^2+9x+2`

Answer 2

`y=4x^2+9x+2`

Explanation:

`y=(x+2)(4x+1)`

Foil the two binomials.

`a=x, b=2, c=4x, d=1`

`y=(x*4x)+(x*1)+(2*4x)+(2*1)`

Simplify.

`y=4x^2+x+8x+2`

Combine like terms.

`y=4x^2+9x+2`