Factor. 4u^2 - 4u + 1 ______

Identify Form: Identify the form of the quadratic trinomial. The given expression 4u^2 - 4u + 1 is a quadratic trinomial in the form of a^2 - 2ab + b^2.Rewrite a^2: Rewrite 4u^2 in the form of a^2. Since 2^2 = 4, we can write 4u^2 as (2u)^2.Rewrite b^2: Rewrite 1 in the form of b^2. Since 1^2 = 1, we can write 1 as (1)^2.Identify a, b: Identify the values of a and b. From the rewritten forms, we have: 4u^2 = (2u)^2 (which implies a = 2u) 1 = (1)^2 (which implies b = 1)Write Factored Form: Write the factored form of the expression 4u^2 - 4u + 1. Since the expression is in the form a^2 - 2ab + b^2, it can be factored as (a - b)^2. Substitute the values of a and b into (a - b)^2 to get the factored form: (2u - 1)^2

Home

Math Problems

Algebra 2

Factor quadratics

Full solution

Q. Factor.

\newline

4u^2 - 4u + 1

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $4u^2 - 4u + 1$ is a quadratic trinomial in the form of $a^2 - 2ab + b^2$ .
Rewrite $a^2$ : Rewrite $4u^2$ in the form of $a^2$ . $\newline$ Since $2^2 = 4$ , we can write $4u^2$ as $(2u)^2$ .
Rewrite $b^2$ : Rewrite $1$ in the form of $b^2$ . $\newline$ Since $1^2 = 1$ , we can write $1$ as $(1)^2$ .
Identify $a, b$ : Identify the values of $a$ and $b$ . $\newline$ From the rewritten forms, we have: $\newline$ $4u^2 = (2u)^2$ (which implies $a = 2u$ ) $\newline$ $1 = (1)^2$ (which implies $b = 1$ )
Write Factored Form: Write the factored form of the expression $4u^2 - 4u + 1$ . Since the expression is in the form $a^2 - 2ab + b^2$ , it can be factored as $(a - b)^2$ . Substitute the values of $a$ and $b$ into $(a - b)^2$ to get the factored form: $(2u - 1)^2$