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(x-3)^(2) Which of the following is equivalent to the given expression? Choose 1 answer: (A) x^(2)+6x+9 (B) x^(2)-6 (C) 2x^(2)+9 (D) x^(2)-6x+9

(x−3)2 (x-3)^{2} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) x2+6x+9 x^{2}+6 x+9 \newline(B) x2−6 x^{2}-6 \newline(C) 2x2+9 2 x^{2}+9 \newline(D) x2−6x+9 x^{2}-6 x+9

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Full solution

Q. (x−3)2 (x-3)^{2} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) x2+6x+9 x^{2}+6 x+9 \newline(B) x2−6 x^{2}-6 \newline(C) 2x2+9 2 x^{2}+9 \newline(D) x2−6x+9 x^{2}-6 x+9
  1. Expand the expression: Expand the given expression using the formula (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2, where a=xa = x and b=3b = 3.\newlineCalculation: (x−3)2=x2−2⋅x⋅3+32=x2−6x+9(x-3)^2 = x^2 - 2\cdot x\cdot 3 + 3^2 = x^2 - 6x + 9
  2. Compare with given choices: Compare the expanded expression with the given choices to find the equivalent one.\newlineCalculation: The expanded expression is x2−6x+9x^2 - 6x + 9.
  3. Match with correct answer: Match the expanded expression to the correct answer choice.\newlineCalculation: The correct answer choice that matches x2−6x+9x^2 - 6x + 9 is (D) x2−6x+9x^2 - 6x + 9.

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