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Factor.\newlinef2+10f+16f^2 + 10f + 16

Full solution

Q. Factor.\newlinef2+10f+16f^2 + 10f + 16
  1. Identify Coefficients: Identify the coefficients for f2f^2, ff, and the constant term in the quadratic expression f2+10f+16f^2 + 10f + 16. Comparing f2+10f+16f^2 + 10f + 16 with the standard quadratic form af2+bf+caf^2 + bf + c, we find that a=1a = 1 (coefficient of f2f^2), b=10b = 10 (coefficient of ff), and c=16c = 16 (constant term).
  2. Find Multiplying Numbers: Determine two numbers that multiply to give c(16)c (16) and add up to give b(10)b (10). We are looking for two numbers that when multiplied give 1616 and when added give 1010. The pair of numbers that satisfy these conditions are 22 and 88 because 2×8=162 \times 8 = 16 and 2+8=102 + 8 = 10.
  3. Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step.\newlineThe factored form of the quadratic expression is (f+2)(f+8)(f + 2)(f + 8) because these two binomials multiply to give the original quadratic expression f2+10f+16f^2 + 10f + 16.