Expand (2x+1)(x+4)

Expand and distribute algebraic expressions using FOIL and distribution.

Expression

Answer

2x^2 + 9x + 4

To expand (2x+1)(x+4), use the FOIL method — multiply each term in the first binomial by each term in the second, then combine like terms.

(2x+1)(x+4)

Step 1 — Apply the FOIL method

FOIL stands for First, Outer, Inner, Last — multiply each pair of terms:

First: 2x · x = 2x²

Outer: 2x · 4 = 8x

Inner: 1 · x = x

Last: 1 · 4 = 4

Step 2 — Add all products and combine like terms

Write out all four products:

2x² + 8x + x + 4

Combine the like terms:

8x + x = 9x

= 2x² + 9x + 4

2x² + 9x + 4

How to expand (2x+1)(x+4)

To expand (2x+1)(x+4), distribute each term across the other factor and combine like terms. The result is 2x^2 + 9x + 4.

This is a algebraic expansion — we multiply out brackets and simplify. For binomials, the FOIL method (First, Outer, Inner, Last) is commonly used.

Frequently asked questions

What is the answer to (2x+1)(x+4)?
The answer is 2x^2 + 9x + 4.

What method is used?
the distributive property (FOIL for two binomials) — multiply each term in one factor by every term in the other, then combine like terms.