What is (3x-2y)^2-(2x-3y)^2 ?

The solution to (3x-2y)^2-(2x-3y)^2 is 5x^2-5y^2

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simplify (3x-2y)^2-(2x-3y)^2

simplify

(3 x - 2 y)^{2} - (2 x - 3 y)^{2}

5 x^{2} - 5 y^{2}

Solution steps

(3 x - 2 y)^{2} - (2 x - 3 y)^{2}

Expand

(3 x - 2 y)^{2} : 9 x^{2} - 12 x y + 4 y^{2}

= 9 x^{2} - 12 x y + 4 y^{2} - (2 x - 3 y)^{2}

Expand

- (2 x - 3 y)^{2} : - 4 x^{2} + 12 x y - 9 y^{2}

= 9 x^{2} - 12 x y + 4 y^{2} - 4 x^{2} + 12 x y - 9 y^{2}

Group like terms

= 9 x^{2} - 4 x^{2} - 12 x y + 12 x y + 4 y^{2} - 9 y^{2}

Add similar elements:

9 x^{2} - 4 x^{2} = 5 x^{2}

= 5 x^{2} - 12 x y + 12 x y + 4 y^{2} - 9 y^{2}

Add similar elements:

- 12 x y + 12 x y = 0

= 5 x^{2} + 4 y^{2} - 9 y^{2}

Add similar elements:

4 y^{2} - 9 y^{2} = - 5 y^{2}

= 5 x^{2} - 5 y^{2}

6 + 2 n = 3

119 - 0.16 \cdot 28 \cdot 9.8 = 28 \cdot x

\frac{1}{2} \cdot 12 \cdot 5

\frac{8}{20} \cdot 100

\frac{1}{2} x = \frac{π}{4}