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Lesson 8: Rewriting Quadratic Expressions in Factored Form (Part 3) Cool Down: Can These Be Rewritten in Factored Form? Write each expression in factored form. If it is not possible, write "not possible:" a^(2)-36 49-25b^(2) c^(2)+9 (100)/(81)-16d^(2)

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Answer

1. (a-6)(a+6) 2. (7-5b)*(7+5b) 3. Not possible 4. (10/(3d)+4) * (10/(3d)-4)

Explanation

This is a factoring and rewriting polynomial expressions problem. Each term is a difference of squares so we attempt to factor each as a difference of squares as follows.A difference of squares is a perfect square subtracted from another, and its usually of the form a²−b²=(a+b)(a−b). We try to factor each expression accordingly.1. We can factor this because it can be written as a difference of squares ✔️ It factors to (a-6)(a+6).2. This can be factored, and can be written as: (7-5b)*(7+5b).3. Factoring formula to a sum or difference of squares does not apply to square and constant added together, thus its not possible.4. It can be factored when we write it as difference of squares forms and take the reciprocals, so we get: (10/3d+4) *(10/3d-4) after simplifying.

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