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

The solution to (2x+3y)^2+(2x-3y)^2 is 8x^2+18y^2

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

simplify

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

8 x^{2} + 18 y^{2}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

4 x^{2} + 4 x^{2} = 8 x^{2}

= 8 x^{2} + 12 x y - 12 x y + 9 y^{2} + 9 y^{2}

Add similar elements:

12 x y - 12 x y = 0

= 8 x^{2} + 9 y^{2} + 9 y^{2}

Add similar elements:

9 y^{2} + 9 y^{2} = 18 y^{2}

= 8 x^{2} + 18 y^{2}

x^{3} + x^{5}

(5 + 15 i) + (20 - 2 i)

(- 9 x^{2} + 3 x - 8) - (3 x^{2} + 8 x)

\frac{5}{3} + \frac{2}{3}