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Factor.\newline16g2+8g+116g^2 + 8g + 1

Full solution

Q. Factor.\newline16g2+8g+116g^2 + 8g + 1
  1. Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (ag+b)2=a2g2+2abg+b2(ag + b)^2 = a^2g^2 + 2abg + b^2. We need to check if 16g2+8g+116g^2 + 8g + 1 fits this pattern.
  2. Identify Square Roots: Identify the square root of the first term and the last term.\newlineThe square root of 16g216g^2 is 4g4g, and the square root of 11 is 11.\newlineSo, we will check if the middle term, 8g8g, is twice the product of 4g4g and 11.\newline2×4g×1=8g2 \times 4g \times 1 = 8g, which matches the middle term.
  3. Write as Perfect Square Trinomial: Write the expression as a perfect square trinomial.\newlineSince the middle term is twice the product of the square roots of the first and last terms, the expression can be written as (4g+1)2(4g + 1)^2.