Factor. 9j^2 - 6j + 1 ______

Identify Form: Identify the form of the quadratic trinomial. The given expression 9j^2 - 6j + 1 is a quadratic trinomial in the form of a^2 - 2ab + b^2.Rewrite a^2: Rewrite 9j^2 in the form of a^2. Since 3^2 = 9, we can express 9j^2 as (3j)^2.Rewrite b^2: Rewrite 1 in the form of b^2. Since 1^2 = 1, we can express 1 as (1)^2.Identify a, b: Identify the values of a and b. By comparing (3j)^2 with a^2 and (1)^2 with b^2, we find that: a = 3j b = 1Substitute Values: Substitute the values of a and b into the form a^2 - 2ab + b^2. Substituting the values of a and b, we get: (3j)^2 - 2 * (3j) * (1) + (1)^2Write Factored Form: Write the factored form of the expression 9j^2 - 6j + 1. Since a^2 - 2ab + b^2 = (a - b)^2, we can write: 9j^2 - 6j + 1 = (3j - 1)^2 Factored form: (3j - 1)^2

Home

Math Problems

Algebra 2

Factor quadratics

Full solution

Q. Factor.

\newline

9j^2 - 6j + 1

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $9j^2 - 6j + 1$ is a quadratic trinomial in the form of $a^2 - 2ab + b^2$ .
Rewrite $a^2$ : Rewrite $9j^2$ in the form of $a^2$ . $\newline$ Since $3^2 = 9$ , we can express $9j^2$ as $(3j)^2$ .
Rewrite $b^2$ : Rewrite $1$ in the form of $b^2$ . $\newline$ Since $1^2 = 1$ , we can express $1$ as $(1)^2$ .
Identify $a, b$ : Identify the values of $a$ and $b$ . By comparing $(3j)^2$ with $a^2$ and $(1)^2$ with $b^2$ , we find that: $a = 3j$ $b = 1$
Substitute Values: Substitute the values of $a$ and $b$ into the form $a^2 - 2ab + b^2$ . $\newline$ Substituting the values of $a$ and $b$ , we get: $\newline$ $(3j)^2 - 2 \times (3j) \times (1) + (1)^2$
Write Factored Form: Write the factored form of the expression $9j^2 - 6j + 1$ . $\newline$ Since $a^2 - 2ab + b^2 = (a - b)^2$ , we can write: $\newline$ $9j^2 - 6j + 1 = (3j - 1)^2$ $\newline$ Factored form: $(3j - 1)^2$