(3x+1)(x+4) In Standard Form

2 min read Jun 16, 2024

Expanding and Simplifying (3x + 1)(x + 4)

This article will walk you through the process of expanding and simplifying the expression (3x + 1)(x + 4) to put it in standard form.

Understanding Standard Form

Standard form for a polynomial (in this case, a quadratic expression) is when the terms are arranged in descending order of their exponents. It looks like this:

ax² + bx + c

where 'a', 'b', and 'c' are constants.

Expanding the Expression

To expand (3x + 1)(x + 4), we use the FOIL method:

First: Multiply the first terms of each binomial: (3x) * (x) = 3x²
Outer: Multiply the outer terms: (3x) * (4) = 12x
Inner: Multiply the inner terms: (1) * (x) = x
Last: Multiply the last terms: (1) * (4) = 4

Now we have: 3x² + 12x + x + 4

Simplifying the Expression

Combine the like terms (12x and x):

3x² + 13x + 4

Final Answer

The expression (3x + 1)(x + 4) in standard form is 3x² + 13x + 4.