Multiply and simplify.

(
3
𝑥
−
2
𝑦
)
2

Question

Multiply and simplify.

(
3
𝑥
−
2
𝑦
)
2

BlackTom AI · Accepted Answer

When expanding (3x − 2y)^2, I recall the square of a binomial formula: (a − b)^2 = a^2 − 2ab + b^2.
Applying this with a = 3x and b = 2y gives: (3x)^2 − 2(3x)(2y) + (2y)^2.
Compute each term: (3x)^2 = 9x^2, 2(3x)(2y) = 12xy, and (2y)^2 = 4y^2.
Putting them together yields 9x^2 − 12xy + 4y^2.

Option A: 6x^2 − 10xy + 4y^2. This deviates in all three coefficients: 6x^2 instead of 9x^2, −10xy instead of −12xy, and the y^2 term is correct in form but paired with the wrong x- and y-coefficients; overall it does not match the correct expansion.

Option B: 9x^2 − 12xy − 4y^2. The first two terms match the correct x^2 and xy coefficients, but the y^2 term has the wrong sign, which invalidates the expression.

Option C: 9x^2 − 4y^2. This expression misses the middle cross term −12xy entirely; also, the separation into a difference of squares is not equivalent to the given square.

Option D: 9x^2 + 4y^2. Here both the cross term and the correct middle term are missing, leaving only the sum of squares; not equal to the original expansion.

Option E: 9x^2 − 12xy + 4y^2. This exactly matches the expansion derived from the binomial square formula, with correct coefficients for all three terms.

Option F: None of these. Since Option E reproduces the correct expansion, this choice would be false because at least one option is correct.

In summary, the correct expansion is the one that aligns with the binomial square result, which is 9x^2 − 12xy + 4y^2, matching Option E. The other options fail because they alter one or more coefficients or omit the necessary cross term, leading to expressions that do not equal the product (3x − 2y)^2.

Multiply and simplify. ( 3 𝑥 − 2 𝑦 ) 2单项选择题

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