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1) x2+6x+9=%0D%0A𝑥%0D%0A2%0D%0A+%0D%0A6%0D%0A𝑥%0D%0A+%0D%0A9%0D%0A=%0D%0A%0D%0A%0D%0A2) x2+10x+25=%0D%0A𝑥%0D%0A2%0D%0A+%0D%0A10%0D%0A𝑥%0D%0A+%0D%0A25%0D%0A=%0D%0A%0D%0A%0D%0A3) 9x2+12x+4=%0D%0A9%0D%0A𝑥%0D%0A2%0D%0A+%0D%0A12%0D%0A𝑥%0D%0A+%0D%0A4%0D%0A=%0D%0A%0D%0A%0D%0A4) 9x2−30x+25=%0D%0A9%0D%0A𝑥%0D%0A2%0D%0A−%0D%0A30%0D%0A𝑥%0D%0A+%0D%0A25%0D%0A=

1 answer

It seems like you have provided several quadratic expressions that resemble perfect square trinomials. Let's analyze each expression:

  1. \( x^2 + 6x + 9 \)

This can be factored as: \[ (x + 3)^2 \] since \( 6x = 2 \cdot 3 \cdot x \) and \( 9 = 3^2 \).

  1. \( x^2 + 10x + 25 \)

This can be factored as: \[ (x + 5)^2 \] since \( 10x = 2 \cdot 5 \cdot x \) and \( 25 = 5^2 \).

  1. \( 9x^2 + 12x + 4 \)

This can be factored as: \[ (3x + 2)^2 \] because \( 12x = 2 \cdot 3 \cdot 2x \) and \( 4 = 2^2 \).

  1. \( 9x^2 - 30x + 25 \)

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:

  1. \( x^2 + 6x + 9 = (x + 3)^2 \)

  2. \( x^2 + 10x + 25 = (x + 5)^2 \)

  3. \( 9x^2 + 12x + 4 = (3x + 2)^2 \)

  4. \( 9x^2 - 30x + 25 = (3x - 5)^2 \)