The expression 9x²−12xy+4y² is a perfect square trinomial. Step 1: Identify the square roots of the first and last terms. The square root of 9x² is 3x. The square root of 4y² is 2y. Step 2: Check the middle term. The middle term of a perfect square trinomial (a−b)² = a² − 2ab + b² should be −2ab. Here, a=3x and b=2y. So, −2ab = −2(3x)(2y) = −12xy. This matches the given middle term. Step 3: Write the factored form. Since it matches the form a² − 2ab + b², it can be factored as (a−b)². Therefore, 9x²−12xy+4y² = (3x−2y)². The factored form of the expression is: (3x−2y)²

(9x²-12xy+4y²)

October 13, 2026Mathematics

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Answer

(3x-2y)^2

Step-by-step solution

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The expression $9x^2-12xy+4y^2$ is a perfect square trinomial.

Identify the square roots of the first and last terms.
The square root of $9x^2$ is $3x$ .
The square root of $4y^2$ is $2y$ .
Check the middle term.
The middle term of a perfect square trinomial $(a-b)^2 = a^2 - 2ab + b^2$ should be $-2ab$ .
Here, $a=3x$ and $b=2y$ .
So, $-2ab = -2(3x)(2y) = -12xy$ .
This matches the given middle term.
Write the factored form.
Since it matches the form $a^2 - 2ab + b^2$ , it can be factored as $(a-b)^2$ .
Therefore, $9x^2-12xy+4y^2 = (3x-2y)^2$ .

The factored form of the expression is:
$(3x-2y)^2$

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(9x²-12xy+4y²)

Answer

Step-by-step solution

Identify the square roots of the first and last terms.

Check the middle term.

Write the factored form.

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