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Factor.\newline25x220x+425x^2 - 20x + 4

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Q. Factor.\newline25x220x+425x^2 - 20x + 4
  1. Check Pattern: Determine if the quadratic expression can be factored using the perfect square trinomial formula.\newlineA perfect square trinomial is in the form (ax)22abx+b2(ax)^2 - 2abx + b^2, which factors to (axb)2(ax - b)^2.\newlineCheck if 25x220x+425x^2 - 20x + 4 fits this pattern.\newline25x225x^2 can be written as (5x)2(5x)^2, and 44 can be written as 222^2.\newlineThe middle term, 20x-20x, should be equal to 2×5x×22 \times 5x \times 2 to fit the pattern.\newline2×5x×2=20x2 \times 5x \times 2 = 20x, which matches the middle term except for the sign.\newlineSo, 25x220x+425x^2 - 20x + 4 is a perfect square trinomial.
  2. Factor Using Formula: Factor the expression using the perfect square trinomial formula.\newlineSince we have (5x)22×5x×2+22(5x)^2 - 2 \times 5x \times 2 + 2^2, the factored form will be (5x2)2(5x - 2)^2.
  3. Write Final Form: Write down the final factored form of the quadratic expression.\newlineThe factored form of 25x220x+425x^2 - 20x + 4 is (5x2)2(5x - 2)^2.