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(w-3)^(5)-(w-3)^(2) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (w-3)^(3) (B) w^(5)-w^(2)-252 (c) (w-3)^(2)(w-3)^(3) (D) (w-3)^(2)((w-3)^(3)-1)

(w−3)5−(w−3)2 (w-3)^{5}-(w-3)^{2} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) (w−3)3 (w-3)^{3} \newline(B) w5−w2−252 w^{5}-w^{2}-252 \newline(C) (w−3)2(w−3)3 (w-3)^{2}(w-3)^{3} \newline(D) (w−3)2((w−3)3−1) (w-3)^{2}\left((w-3)^{3}-1\right)

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Full solution

Q. (w−3)5−(w−3)2 (w-3)^{5}-(w-3)^{2} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) (w−3)3 (w-3)^{3} \newline(B) w5−w2−252 w^{5}-w^{2}-252 \newline(C) (w−3)2(w−3)3 (w-3)^{2}(w-3)^{3} \newline(D) (w−3)2((w−3)3−1) (w-3)^{2}\left((w-3)^{3}-1\right)
  1. Analyze Given Options: To find the equivalent expression, we need to analyze the given options and see which one matches the original expression after simplification.
  2. Check Option (A): Option (A) suggests that w\(-3)^{55}-(w−3-3)^{22}\ is equivalent to w\(-3)^{33}\. To check this, we would need to factor out the common term from the original expression, which is w\(-3)^{22}\. However, this would leave us with w\(-3)^{33} - 11\, not just w\(-3)^{33}\. Therefore, option (A) is incorrect.
  3. Check Option (B): Option (B) suggests that (w−3)5−(w−3)2(w-3)^{5}-(w-3)^{2} is equivalent to w5−w2−252w^{5}-w^{2}-252. This option does not factor out the common term and instead expands the expression incorrectly, as it does not account for the binomial expansion of (w−3)5(w-3)^{5} and (w−3)2(w-3)^{2}. Therefore, option (B) is incorrect.
  4. Check Option (C): Option (C) suggests that (w−3)5−(w−3)2(w-3)^{5}-(w-3)^{2} is equivalent to (w−3)2(w−3)3(w-3)^{2}(w-3)^{3}. This is the factored form of the original expression, using the property of exponents that states am−n=am/ana^{m-n} = a^{m}/a^{n}. Therefore, (w−3)5/(w−3)2=(w−3)3(w-3)^{5}/(w-3)^{2} = (w-3)^{3}, and when multiplied by (w−3)2(w-3)^{2}, it gives us the original expression. Thus, option (C) is correct.
  5. Check Option (D): Option (D) suggests that w-3)^{5}-(w-3)^{2}\ is equivalent to \$w-3)^{2}((w-3)^{3}-1)\. This option is similar to option (A) but includes the subtraction of \$1 inside the parentheses. This option is incorrect because it implies an additional subtraction of w\(-3)^{22}\ which is not present in the original expression.

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