Expand (x-1)(x^2+x+1)
Expand and distribute algebraic expressions using FOIL and distribution.
To expand (x-1)(x^2+x+1), use the FOIL method — multiply each term in the first binomial by each term in the second, then combine like terms.
(x-1)(x2+x+1)
FOIL stands for First, Outer, Inner, Last — multiply each pair of terms:
First: x · x = x2
Outer: x · x2 = x3
Inner: -1 · x = -x
Last: -1 · x2 = -x2
Write out all four products:
x2 + x3 − x − x2
Combine the like terms:
x2 − x2 = 0
= x3 − 1
x3 − 1
How to expand (x-1)(x^2+x+1)
To expand (x-1)(x^2+x+1), distribute each term across the other factor and combine like terms. The result is x^3 − 1.
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-1)(x^2+x+1)?
The answer is x^3 − 1.
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.