(x-10)^(2) Which of the following is equivalent to the given expression? Choose 1 answer: (A) x^(2)+100 (B) 2x^(2)-20 x+100 (c) x^(2)-20 x+100 (D) x^(2)-20 x-20

Expand the expression: Expand the expression (x-10)^(2) using the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a is x and b is 10. So, (x-10)^2 = x^2 - 2*x*10 + 10^2.Calculate the terms: Calculate the terms individually. First term: x^2 remains the same. Second term: -2*x*10 simplifies to -20x. Third term: 10^2 simplifies to 100. So, (x-10)^2 = x^2 - 20x + 100.Compare the expanded expression: Compare the expanded expression with the given choices. The expanded expression is x^2 - 20x + 100. This matches with choice (C) x^2 - 20x + 100.

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Math Problems

Algebra 1

Negative exponents

Full solution

(x-10)^{2}

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Which of the following is equivalent to the given expression?

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Choose

1

answer:

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(A)

x^{2}+100

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(B)

2 x^{2}-20 x+100

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(C)

x^{2}-20 x+100

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(D)

x^{2}-20 x-20

Expand the expression: Expand the expression $(x-10)^{2}$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$ . $\newline$ Here, $a$ is $x$ and $b$ is $10$ . $\newline$ So, $(x-10)^2 = x^2 - 2 \times x \times 10 + 10^2$ .
Calculate the terms: Calculate the terms individually. $\newline$ First term: $x^2$ remains the same. $\newline$ Second term: $-2 \times x \times 10$ simplifies to $-20x$ . $\newline$ Third term: $10^2$ simplifies to $100$ . $\newline$ So, $(x-10)^2 = x^2 - 20x + 100$ .
Compare the expanded expression: Compare the expanded expression with the given choices. $\newline$ The expanded expression is $x^2 - 20x + 100$ . $\newline$ This matches with choice (C) $x^2 - 20x + 100$ .