Question

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

Answer 1

`y=x^2+7x+12`

Explanation:

A polynomial is in standard form if it is written with all the `x^2`, `x`, and constant terms together.

It's typically written as

`y=ax^2+bx+c`

where `a,b,` and `c` are all constants that can vary.

Standard form is useful because it generalizes how to find the roots of any quadratic equation through the quadratic formula (`x=(-b+-sqrt(b^2-4ac))/(2a`).

In your case, to find the standard version of the equation, distribute the two binomials through the " FOIL " method.

FOIL stands for F irst, O uter, I nner, L ast. These are the four different combinations of terms you can multiply when you have two binomials.

First: multiply the first term in each binomial
`(color(red)x+3)(color(red)x+4)`
`=x^2`

Outer: multiply the terms on the outside
`(color(red)x+3)(x+color(red)4)`
`=4x`

Inner: multiply the terms on the inside
`(x+color(red)3)(color(red)x+4)`
`=3x`

Last: multiply the last term in each binomial
`(x+color(red)3)(x+color(red)4)`
`=12`

Now, add all the different products.

`y=x^2+4x+3x+12`

Combine like terms.

`y=x^2+7x+12`

This is in the standard form of the quadratic equation `y=ax^2+bx+c`, where `a=1,b=7,c=12`.