Expand the expression (x-1)^2
Understand the Problem
The image shows the mathematical expression (x-1)^2. Assuming the question is to expand the expression, we will use the binomial theorem or simply multiply (x-1) by itself.
Answer
$x^2 - 2x + 1$
Answer for screen readers
$x^2 - 2x + 1$
Steps to Solve
- Rewrite the expression
Recognize that $(x-1)^2$ means $(x-1)$ multiplied by itself.
$$(x-1)^2 = (x-1)(x-1)$$
- Apply the distributive property (also known as the FOIL method)
Multiply each term in the first parenthesis by each term in the second parenthesis:
$$ (x-1)(x-1) = xx + x(-1) + (-1)x + (-1)(-1) $$
- Simplify the multiplied terms
Multiply the terms:
$$ xx = x^2 $$ $$ x(-1) = -x $$ $$ (-1)x = -x $$ $$ (-1)(-1) = 1 $$
- Combine the simplified terms
Combine all the terms to form the expanded expression:
$$ x^2 - x - x + 1 $$
- Combine like terms
Combine the $-x$ terms:
$$ x^2 - 2x + 1 $$
$x^2 - 2x + 1$
More Information
The expression $(x-1)^2$ is a perfect square trinomial. Perfect square trinomials follow the pattern $(a - b)^2 = a^2 - 2ab + b^2$.
Tips
A common mistake is to incorrectly apply the exponent, thinking that $(x-1)^2$ is equal to $x^2 - 1^2 = x^2 - 1$. Remember to expand the expression as $(x-1)(x-1)$ and use the distributive property (FOIL method) correctly. Another common mistake is an error with signs (forgetting that a negative times a negative is a positive).
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