Factor 81x^2+72x+16

Problem

81*x2+72*x+16

Solution

1. Identify the structure of the expression as a potential perfect square trinomial of the form a2+2*a*b+b2

2. Determine the square root of the first term, 81*x2 which is 9*x Let a=9*x

3. Determine the square root of the last term, 16 which is 4 Let b=4

4. Verify the middle term by calculating 2*a*b

2*(9*x)*(4)=72*x

5. Apply the perfect square trinomial formula (a+b)2

(9*x+4)2

Final Answer

81*x2+72*x+16=(9*x+4)2

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