Expand (x-4)(x+7)

Expand and distribute algebraic expressions using FOIL and distribution.

Expression

Answer

x^2 + 3x − 28

To expand (x-4)(x+7), use the FOIL method — multiply each term in the first binomial by each term in the second, then combine like terms.

(x-4)(x+7)

Step 1 — Apply the FOIL method

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

First: x · x = x²

Outer: x · 7 = 7x

Inner: -4 · x = -4x

Last: -4 · 7 = -28

Step 2 — Add all products and combine like terms

Write out all four products:

x² + 7x − 4x − 28

Combine the like terms:

7x − 4x = 3x

= x² + 3x − 28

x² + 3x − 28

How to expand (x-4)(x+7)

To expand (x-4)(x+7), distribute each term across the other factor and combine like terms. The result is x^2 + 3x − 28.

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 (x-4)(x+7)?
The answer is x^2 + 3x − 28.

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.