What is (3x-5y)^2-2(3x-5y)(7y-11x)+(7y-11x)^2 ?

The solution to (3x-5y)^2-2(3x-5y)(7y-11x)+(7y-11x)^2 is 196x^2-336xy+144y^2

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simplify (3x-5y)^2-2(3x-5y)(7y-11x)+(7y-11x)^2

simplify

(3 x - 5 y)^{2} - 2 (3 x - 5 y) (7 y - 11 x) + (7 y - 11 x)^{2}

196 x^{2} - 336 x y + 144 y^{2}

Solution steps

(3 x - 5 y)^{2} - 2 (3 x - 5 y) (7 y - 11 x) + (7 y - 11 x)^{2}

Expand

(3 x - 5 y)^{2} : 9 x^{2} - 30 x y + 25 y^{2}

= 9 x^{2} - 30 x y + 25 y^{2} - 2 (3 x - 5 y) (7 y - 11 x) + (7 y - 11 x)^{2}

Expand

- 2 (3 x - 5 y) (7 y - 11 x) : 66 x^{2} - 152 x y + 70 y^{2}

= 9 x^{2} - 30 x y + 25 y^{2} + 66 x^{2} - 152 x y + 70 y^{2} + (7 y - 11 x)^{2}

Expand

(7 y - 11 x)^{2} : 49 y^{2} - 154 x y + 121 x^{2}

= 9 x^{2} - 30 x y + 25 y^{2} + 66 x^{2} - 152 x y + 70 y^{2} + 49 y^{2} - 154 x y + 121 x^{2}

Group like terms

= 9 x^{2} + 66 x^{2} + 121 x^{2} - 30 x y - 152 x y - 154 x y + 25 y^{2} + 70 y^{2} + 49 y^{2}

Add similar elements:

9 x^{2} + 66 x^{2} + 121 x^{2} = 196 x^{2}

= 196 x^{2} - 30 x y - 152 x y - 154 x y + 25 y^{2} + 70 y^{2} + 49 y^{2}

Add similar elements:

- 30 x y - 152 x y - 154 x y = - 336 x y

= 196 x^{2} - 336 x y + 25 y^{2} + 70 y^{2} + 49 y^{2}

Add similar elements:

25 y^{2} + 70 y^{2} + 49 y^{2} = 144 y^{2}

= 196 x^{2} - 336 x y + 144 y^{2}

- x^{2} + 5 x = 0

\frac{x - 2}{3} > 2

x^{3} + 5 x^{2} - 17 x - 21

7 = x^{2}

(\frac{2}{3} x \frac{2}{3})^{3}

What is (3x-5y)^2-2(3x-5y)(7y-11x)+(7y-11x)^2 ?
The solution to (3x-5y)^2-2(3x-5y)(7y-11x)+(7y-11x)^2 is 196x^2-336xy+144y^2