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

The solution to (3x-y)^2-(2x-3y)^2 is 5x^2+6xy-8y^2

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

simplify

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

5 x^{2} + 6 x y - 8 y^{2}

Solution steps

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

Expand

(3 x - y)^{2} : 9 x^{2} - 6 x y + y^{2}

= 9 x^{2} - 6 x y + 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} - 6 x y + y^{2} - 4 x^{2} + 12 x y - 9 y^{2}

Group like terms

= 9 x^{2} - 4 x^{2} - 6 x y + 12 x y + y^{2} - 9 y^{2}

Add similar elements:

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

= 5 x^{2} - 6 x y + 12 x y + y^{2} - 9 y^{2}

Add similar elements:

- 6 x y + 12 x y = 6 x y

= 5 x^{2} + 6 x y + y^{2} - 9 y^{2}

Add similar elements:

y^{2} - 9 y^{2} = - 8 y^{2}

= 5 x^{2} + 6 x y - 8 y^{2}

4 \cdot (2 - 5 x)

9 x^{2} y^{2} - 6 x y - y^{2}

(\frac{x ^{2}}{2}) - (\frac{x}{6})

\frac{5 m ^{2} + 22 m + 21 - ( 4 m + 10 )}{3}

2 sin^{2} (x) - 2 (sin (x) - cos (x)) + 1

What is (3x-y)^2-(2x-3y)^2 ?
The solution to (3x-y)^2-(2x-3y)^2 is 5x^2+6xy-8y^2