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Factor.\newlinen2+8n+16n^2 + 8n + 16

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Q. Factor.\newlinen2+8n+16n^2 + 8n + 16
  1. Check Perfect Square Trinomial: Determine if the quadratic can be factored using the perfect square trinomial formula.\newlineA perfect square trinomial is in the form (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2. We need to check if n2+8n+16n^2 + 8n + 16 fits this pattern.
  2. Identify Square Roots: Identify the square root of the first term and the last term.\newlineThe square root of n2n^2 is nn, and the square root of 1616 is 44. So, we have potential candidates for aa and bb in the perfect square trinomial formula: a=na = n and b=4b = 4.
  3. Verify Middle Term: Check if the middle term fits the formula 2ab2ab. For our candidates a=na = n and b=4b = 4, the middle term should be 2×n×4=8n2 \times n \times 4 = 8n. This matches the middle term of our quadratic expression.
  4. Write Factored Form: Write the factored form using the perfect square trinomial formula.\newlineSince the expression fits the pattern of a perfect square trinomial, we can write it as (n+4)2(n + 4)^2.