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

The solution to (x+2y)^2-(3x-y)^2 is -8x^2+10xy+3y^2

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

simplify

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

- 8 x^{2} + 10 x y + 3 y^{2}

Solution steps

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

Expand

(x + 2 y)^{2} : x^{2} + 4 x y + 4 y^{2}

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

Expand

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

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

Group like terms

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

Add similar elements:

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

= - 8 x^{2} + 4 x y + 6 x y + 4 y^{2} - y^{2}

Add similar elements:

4 x y + 6 x y = 10 x y

= - 8 x^{2} + 10 x y + 4 y^{2} - y^{2}

Add similar elements:

4 y^{2} - y^{2} = 3 y^{2}

= - 8 x^{2} + 10 x y + 3 y^{2}

w^{2} + 8 w + 12

3 \frac{3}{4} \div 2

2^{0.9}

\frac{3 x}{2} + \frac{8}{3}

What is (x+2y)^2-(3x-y)^2 ?
The solution to (x+2y)^2-(3x-y)^2 is -8x^2+10xy+3y^2