Simplify: ${(2 x - 3 y)}^{2} + 12 x y$

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Solution

Using the identity: $(x - y)^{2} = x^{2} + y^{2} - 2 x y$ .

Given: ${(2 x - 3 y)}^{2} + 12 x y$
We apply the above identity as follows:

${(2 x - 3 y)}^{2} + 12 x y = [{(2 x)}^{2} + {(3 y)}^{2} - (2 \times 2 x \times 3 y)] + 12 x y$
$= 4 x^{2} + 9 y^{2} - 12 x y + 12 x y$
$= 4 x^{2} + 9 y^{2}$

Hence, ${(2 x - 3 y)}^{2} + 12 x y = 4 x^{2} + 9 y^{2}$ .

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Similar questions

(2 x + \frac{1}{3 y})^{2} - (2 x - \frac{1}{3 y})^{2}

(2 x + 3 y)^{2}

2 x + 3 x y + 2 y + 3 y^{2}

Four alternative options are given for each of the following statements. Select the correct option.

The expansion of (2x − 3y)² is:

A. 2x² + 3y² + 6xy

B. 4x² + 9y² − 12xy

C. 2x² + 3y² − 6xy

D. 4x² + 9y² + 12xy

2 x y + 9 x^{2}

12 x y + 4 x^{2} - 3 y^{2}

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