Factor x^2+8xy+16y^2

Problem

x2+8*x*y+16*y2

Solution

1. Identify the structure of the expression as a quadratic trinomial in the form a2+2*a*b+b2

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

3. Find the first term a by taking the square root of x2

a=√(,x2)=x

4. Find the second term b by taking the square root of 16*y2

b=√(,16*y2)=4*y

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

2*(x)*(4*y)=8*x*y

6. Apply the perfect square trinomial formula a2+2*a*b+b2=(a+b)2

(x+4*y)2

Final Answer

x2+8*x*y+16*y2=(x+4*y)2

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