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. We need to check if 4w2−20w+25 fits this pattern.
Find Square Roots: Find the square root of the first term and the last term.The square root of 4w2 is 2w, and the square root of 25 is 5.So, we will check if the middle term is twice the product of 2w and 5.
Calculate Middle Term: Calculate twice the product of 2w and 5. 2×2w×5=20w. The middle term of our quadratic is −20w, which matches the calculated value, but with a negative sign. This suggests that our trinomial is a perfect square trinomial.
Write Factored Form: Write the factored form as a square of a binomial.Since the middle term is negative, our binomial will have a subtraction sign.The factored form is 2w−5^2.
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