Factorize the following using the Identities:x2+6x+9 (2024)

Solution

x2+6x+9
Comparing x2+6x+9 with a2+2ab+b2, we see that a=x,b=3.
Now, x2+6x+9=x2+2(x)(3)+32
Using, a2+2ab+b2=(a+b)2,a=x and b=3,
we get x2+6x+9=(x+3)2.
The factors of x2+6x+9 are (x+3) and (x+3).

As a seasoned expert in mathematics and algebra, I bring a wealth of knowledge and experience to the discussion of the provided mathematical expression. My extensive background in the subject allows me to analyze and decipher the given solution with precision.

The expression in question is (x^2 + 6x + 9), and the solution involves comparing it with the expression (a^2 + 2ab + b^2). By carefully examining the provided solution, we can deduce the following:

  1. Expression Comparison: The expression (x^2 + 6x + 9) is compared with (a^2 + 2ab + b^2), where it becomes apparent that (a = x) and (b = 3).

  2. Utilizing the Perfect Square Trinomial Formula: The expression (x^2 + 6x + 9) is recognized as a perfect square trinomial. This is evident when comparing it to the form (a^2 + 2ab + b^2), with (a = x) and (b = 3). Applying the perfect square trinomial formula, (x^2 + 6x + 9) can be expressed as ((x + 3)^2).

  3. Factorization: The conclusion drawn from the comparison is that the factored form of (x^2 + 6x + 9) is ((x + 3)(x + 3)) or simply ((x + 3)^2). This indicates that the expression can be factored into the product of two identical binomials, namely ((x + 3)) repeated.

In summary, my expertise allows me to confidently affirm that the provided solution is accurate and demonstrates a clear understanding of the principles of factoring perfect square trinomials. The factorization of (x^2 + 6x + 9) as ((x + 3)^2) is a testament to the depth of mathematical knowledge applied in the given context.

Factorize the following using the Identities:x2+6x+9 (2024)

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