Factor 9x^2+48x+64

Problem

9*x^2+48*x+64

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a^2+2*a*b+b^2

2. Determine the square roots of the first and last terms.

3. Calculate the first term's root: √(,9*x^2)=3*x

4. Calculate the last term's root: √(,64)=8

5. Verify the middle term by checking if 2*a*b matches 48*x

2*(3*x)*(8)=48*x

6. Apply the formula for a perfect square trinomial (a+b)^2

(3*x+8)^2

Final Answer

9*x^2+48*x+64=(3*x+8)^2

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