Questions: 16a^2-24a+9

16a^2-24a+9
Transcript text: \[ 16 a^{2}-24 a+9= \]
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Solution

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Solution Steps

Solution Approach

The given expression 16a224a+916a^2 - 24a + 9 is a quadratic expression. To factor it, we can recognize it as a perfect square trinomial. A perfect square trinomial takes the form (ax+b)2=a2x2+2abx+b2(ax + b)^2 = a^2x^2 + 2abx + b^2. We need to identify aa and bb such that the expression matches this form.

Step 1: Identify the Expression

We start with the quadratic expression given by

16a224a+9. 16a^2 - 24a + 9.

Step 2: Recognize the Perfect Square Trinomial

We can observe that this expression can be factored as a perfect square trinomial. A perfect square trinomial has the form

(ax+b)2=a2x2+2abx+b2. (ax + b)^2 = a^2x^2 + 2abx + b^2.

Step 3: Factor the Expression

Upon factoring, we find that

16a224a+9=(4a3)2. 16a^2 - 24a + 9 = (4a - 3)^2.

Final Answer

Thus, the factored form of the expression is

(4a3)2. \boxed{(4a - 3)^2}.

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