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

The solution to (2x+y)^2-(3y-z)^2 is 4x^2+4xy-8y^2+6yz-z^2

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

simplify

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

4 x^{2} + 4 x y - 8 y^{2} + 6 yz - z^{2}

Solution steps

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

Expand

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

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

Expand

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

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

Add similar elements:

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

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

\frac{8}{3} - \frac{1}{6}

3 x^{3} - 16 x^{2} + 12 x + 16

\frac{\frac{4 x - 24}{- 3 x - 15}}{\frac{x ^{2} - 36}{x + 5}}

\frac{4}{3} (- 6 Y)

What is (2x+y)^2-(3y-z)^2 ?
The solution to (2x+y)^2-(3y-z)^2 is 4x^2+4xy-8y^2+6yz-z^2