(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)

Question

(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)

Bytelearn · Accepted Answer

Understand the Expression: To solve the given problem, we first need to understand the expression and what is being asked. The expression is (w-3)^(5)-(w-3)^(2). We are asked to find an equivalent expression among the given options.Factor Common Base: We recognize that both terms in the expression have a common base of (w-3) but with different exponents. This suggests that we might be able to factor the expression using properties of exponents.Apply Exponent Property: We apply the property of exponents that states a^(m) - a^(n) = a^(n)(a^(m-n) - 1) to the given expression. Here, a = (w-3), m = 5, and n = 2. So, we get (w-3)^(2)((w-3)^(5-2) - 1).Simplify Inside Parentheses: Simplifying the expression inside the parentheses gives us (w-3)^(2)((w-3)^(3) - 1). This matches one of the given options directly.Find Equivalent Expression: Therefore, the equivalent expression to the given expression (w-3)^(5)-(w-3)^(2) is (w-3)^(2)((w-3)^(3)-1), which corresponds to option (D).

$(w-3)^{5}-(w-3)^{2}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $(w-3)^{3}$ $\newline$ (B) $w^{5}-w^{2}-252$ $\newline$ (C) $(w-3)^{2}(w-3)^{3}$ $\newline$ (D) $(w-3)^{2}((w-3)^{3}-1)$

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