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Factor.\newline4w220w+254w^2 - 20w + 25

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Q. Factor.\newline4w220w+254w^2 - 20w + 25
  1. Identify Perfect Square Trinomial: Identify if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (aw+b)2=a2w2+2abw+b2(aw + b)^2 = a^2w^2 + 2abw + b^2. We need to check if 4w220w+254w^2 - 20w + 25 fits this pattern.
  2. Find Square Roots: Find the square root of the first term and the last term.\newlineThe square root of 4w24w^2 is 2w2w, and the square root of 2525 is 55.\newlineSo, we will check if the middle term is twice the product of 2w2w and 55.
  3. Calculate Middle Term: Calculate twice the product of 2w2w and 55. \newline2×2w×5=20w2 \times 2w \times 5 = 20w. \newlineThe middle term of our quadratic is 20w-20w, which matches the calculated value, but with a negative sign. \newlineThis suggests that our trinomial is a perfect square trinomial.
  4. Write Factored Form: Write the factored form as a square of a binomial.\newlineSince the middle term is negative, our binomial will have a subtraction sign.\newlineThe factored form is 2w52w - 5^22.