Factor. 9r^2 - 12r + 4 ______

Identify Form: Identify the form of the quadratic trinomial. 9r^2 - 12r + 4 represents the form a^2 - 2ab + b^2. Rewrite Quadratic: Rewrite 9r^2 in the form of a^2. 3^2 = 9 9r^2 = (3r)^2Identify Values: Rewrite 4 in the form of b^2. 2^2 = 4Substitute Values: We found: 9r^2 = (3r)^2 4 = 2^2 Identify the values of a and b. Compare (3r)^2 with a^2 and 2^2 with b^2. a = 3r b = 2Equivalent Expression: We found: 9r^2 - 12r + 4 represents the form a^2 - 2ab + b^2. Identify the equivalent expression after substituting the values of a and b. Substitute the values of a and b in a^2 - 2ab + b^2 Equivalent expression: (3r)^2 - 2 * (3r) * (2) + 2^2Write Factored Form: Write the factored form of the expression 9r^2 - 12r + 4. a^2 - 2ab + b^2 = (a - b)^2 9r^2 - 12r + 4 = (3r - 2)^2 Factored form: (3r - 2)^2

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Algebra 2

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Q. Factor.

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9r^2 - 12r + 4

Identify Form: Identify the form of the quadratic trinomial. $9r^2 - 12r + 4$ represents the form $a^2 - 2ab + b^2$ .
Rewrite Quadratic: Rewrite $9r^2$ in the form of $a^2$ . $\newline$ $3^2 = 9$ $\newline$ $9r^2 = (3r)^2$
Identify Values: Rewrite $4$ in the form of $b^2$ . $\newline$ $2^2 = 4$
Substitute Values: We found: $\newline$ $9r^2 = (3r)^2$ $\newline$ $4 = 2^2$ $\newline$ Identify the values of $a$ and $b$ . $\newline$ Compare $(3r)^2$ with $a^2$ and $2^2$ with $b^2$ . $\newline$ $a = 3r$ $\newline$ $b = 2$
Equivalent Expression: We found: $\newline$ $9r^2 - 12r + 4$ represents the form $a^2 - 2ab + b^2$ . $\newline$ Identify the equivalent expression after substituting the values of $a$ and $b$ . $\newline$ Substitute the values of $a$ and $b$ in $a^2 - 2ab + b^2$ $\newline$ Equivalent expression: $(3r)^2 - 2 \times (3r) \times (2) + 2^2$
Write Factored Form: Write the factored form of the expression $9r^2 - 12r + 4$ . $\newline$ $a^2 - 2ab + b^2 = (a - b)^2$ $\newline$ $9r^2 - 12r + 4 = (3r - 2)^2$ $\newline$ Factored form: $(3r - 2)^2$