It seems like you have provided several quadratic expressions that resemble perfect square trinomials. Let's analyze each expression:
- \( x^2 + 6x + 9 \)
This can be factored as: \[ (x + 3)^2 \] since \( 6x = 2 \cdot 3 \cdot x \) and \( 9 = 3^2 \).
- \( x^2 + 10x + 25 \)
This can be factored as: \[ (x + 5)^2 \] since \( 10x = 2 \cdot 5 \cdot x \) and \( 25 = 5^2 \).
- \( 9x^2 + 12x + 4 \)
This can be factored as: \[ (3x + 2)^2 \] because \( 12x = 2 \cdot 3 \cdot 2x \) and \( 4 = 2^2 \).
- \( 9x^2 - 30x + 25 \)
This can be factored as: \[ (3x - 5)^2 \] since \( -30x = 2 \cdot 15 \cdot x \) and \( 25 = 5^2 \).
In summary, the factored forms of the given quadratics are:
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\( x^2 + 6x + 9 = (x + 3)^2 \)
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\( x^2 + 10x + 25 = (x + 5)^2 \)
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\( 9x^2 + 12x + 4 = (3x + 2)^2 \)
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\( 9x^2 - 30x + 25 = (3x - 5)^2 \)