Select the correct answer for:

Simplify
(
𝑥
−
3
)
2

Question

Select the correct answer for:

Simplify  
(
𝑥
−
3
)
2

BlackTom AI · Accepted Answer

Let's break down the task by first remembering how to square a binomial: (a - b)^2 = a^2 - 2ab + b^2.

Option 1: x^2 − 6x + 9. Here, a = x and b = 3, so applying the rule gives x^2 − 2·x·3 + 3^2 = x^2 − 6x + 9. This matches the expansion precisely.

Option 2: x^2 − 6x − 9. This would require the constant term to be −9, which would only happen if the square produced 9 with a negative sign in front of it, but in a squared binomial the constant term is always nonnegative (3^2 = 9). Thus this option misplaces the sign of the constant term.

Option 3: x^2 − 3x + 9. Here, the middle term should be −6x, not −3x, because 2ab with a = x and b = 3 yields 6x. The incorrect coefficient in the linear term signals a miscalculation in the cross product.

Option 4: x^2 + 6x + 9. This has +6x, which would arise if the binomial were (x + 3)^2 rather than (x − 3)^2. Since the original expression uses a subtraction, the linear term should be negative, not positive.

Option 5: x^2 − 9. This resembles the difference of squares pattern (a^2 − b^2) rather than a perfect square expansion. It would correspond to (x − 3)(x + 3), not to (x − 3)^2, so it does not match the given expression.

In summary, by applying the standard expansion for (x − 3)^2 and checking signs and coefficients, we see which candidate aligns with x^2 − 6x + 9 and which do not. The mismatches in the linear term or constant term in the other options reveal common algebraic slips, such as miscomputing 2ab or misplacing signs in a squared binomial.

Select the correct answer for: Simplify ( 𝑥 − 3 ) 2单项选择题

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