Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $w^2 - 2w + 1$

View step-by-step help

View step-by-step help

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

w^2 - 2w + 1

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ . We can compare $w^2 - 2w + 1$ to the form $a^2 - 2ab + b^2$ to see if it matches.
Identify $a$ and $b$ : Identify $a$ and $b$ in the expression $w^2 - 2w + 1$ . Here, $a = w$ and $b = 1$ because $(w)^2 = w^2$ and $(1)^2 = 1$ . The middle term $-2w$ should be equal to $b$ $0$ , which is $b$ $1$ .
Confirm Trinomial Type: Confirm that the expression is a perfect square trinomial. $\newline$ Since $w^2$ is the square of $w$ , $1$ is the square of $1$ , and $-2w$ is twice the product of $w$ and $1$ , the expression $w^2 - 2w + 1$ is indeed a perfect square trinomial.
Factor Using Formula: Factor the expression using the perfect square trinomial formula. $\newline$ The factored form of $w^2 - 2w + 1$ is $(w - 1)^2$ because $(w - 1)(w - 1)$ gives $w^2 - w - w + 1$ , which simplifies to $w^2 - 2w + 1$ .

More problems from Factor quadratics: special cases

Question

Find the greatest common factor.

\newline

9v^3, 6v^3

\newline

\newline

Write your answer as a constant times a product of single variables raised to exponents.

\newline

\underline{\hspace{1cm}}

Posted 1 month ago

Question

Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

6x^3 + 9x^2

\newline

Posted 2 months ago

Question

\newline

k^2 + 9k + 18

\newline

Posted 1 month ago

Question

\newline

9j^2 - 16

\newline

Posted 1 month ago

Question

\newline

j^3 + 2j^2 + 5j + 10

Posted 2 months ago

Question

x^4 + 6x^2 + 9

\newline

All factors in your answer should have integer coefficients.

\newline

Posted 2 months ago

Question

\newline

z^2 + 13z + 22

\newline

Posted 1 month ago

Question

Simplify the expression:

\newline

5x + 9x - 4x - 2x

\newline

Posted 3 months ago

Question

3 - 3^2

Posted 3 months ago

Question

5 - 5^2

Posted 1 month ago