Factor x^2+8x+16

Problem

x2+8*x+16

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=1 b=8 and c=16

2. Find two numbers that multiply to the constant term c=16 and add up to the linear coefficient b=8

3. Determine that the numbers are 4 and 4 since 4⋅4=16 and 4 + 4 = 8$.

4. Recognize that because the two numbers are identical, the expression is a perfect square trinomial of the form (x+r)2

5. Rewrite the expression in its factored form (x+4)*(x+4) which simplifies to (x+4)2

Final Answer

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

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