6. The expression (3x - 2y)^2 is equivalent to:

Question

A. 9x^2 + 4y^2
B. 6x^2 - 4y^2
C. 9x^2 - 12xy - 4y^2
D. 9x^2 - 12xy + 4y^2
E. 6x^2 - 10xy - 4y^2

Answer 1

To expand the expression \((3x - 2y)^2\), we can use the formula for the square of a binomial:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

In this case, \(a = 3x\) and \(b = 2y\). Applying the formula, we have:

\[ (3x - 2y)^2 = (3x)^2 - 2(3x)(2y) + (2y)^2 \]

Calculating each term:

1. \((3x)^2 = 9x^2\)
2. \(-2(3x)(2y) = -12xy\)
3. \((2y)^2 = 4y^2\)

Putting it all together:

\[ (3x - 2y)^2 = 9x^2 - 12xy + 4y^2 \]

Now looking at the options provided, the expression we derived matches:

D. \(9x^2 - 12xy + 4y^2\)

So the answer is D.