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(x+6)^(2)
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
x^(2)+12 x+12
(B)
2x^(2)+12 x+12
(c)
x^(2)+12 x+36
(D)
2x^(2)+12

$(x+6)^{2}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $x^{2}+12 x+12$ $\newline$ (B) $2 x^{2}+12 x+12$ $\newline$ (C) $x^{2}+12 x+36$ $\newline$ (D) $2 x^{2}+12$

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Compare linear and exponential growth

Full solution

Q.

(x+6)^{2}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

x^{2}+12 x+12

\newline

(B)

2 x^{2}+12 x+12

\newline

(C)

x^{2}+12 x+36

\newline

(D)

2 x^{2}+12

Applying the formula: We apply the formula to the given expression: $\newline$ $(x+6)^2 = x^2 + 2 \cdot x \cdot 6 + 6^2$ $\newline$ Now we calculate each term: $\newline$ $x^2$ is the square of $x$ , $\newline$ $2 \cdot x \cdot 6$ is the product of $2$ , $x$ , and $6$ , $\newline$ $6^2$ is the square of $6$ .
Calculating each term: Performing the calculations: $\newline$ $x^2 = x^2$ (no change), $\newline$ $2 \times x \times 6 = 12x$ (multiplying $2$ by $x$ and then by $6$ ), $\newline$ $6^2 = 36$ (squaring $6$ ). $\newline$ So, $(x+6)^2 = x^2 + 12x + 36$ .
Performing the calculations: We compare the result with the given choices: $\newline$ (A) $x^2 + 12x + 12$ (incorrect, the constant term should be $36$ ), $\newline$ (B) $2x^2 + 12x + 12$ (incorrect, the coefficient of $x^2$ should be $1$ and the constant term should be $36$ ), $\newline$ (C) $x^2 + 12x + 36$ (correct, matches our expanded expression), $\newline$ (D) $2x^2 + 12$ (incorrect, the coefficient of $x^2$ should be $1$ and the constant term is missing).

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