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

Problem

x^2+8*x*y+16*y^2

Solution

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

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

3. Find the first term a by taking the square root of x^2

a=√(,x^2)=x

4. Find the second term b by taking the square root of 16*y^2

b=√(,16*y^2)=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 a^2+2*a*b+b^2=(a+b)^2

(x+4*y)^2

Final Answer

x^2+8*x*y+16*y^2=(x+4*y)^2

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