What is [3(2x-3y)]^2+[4(2x+3y)]^2 ?

The solution to [3(2x-3y)]^2+[4(2x+3y)]^2 is 100x^2+84xy+225y^2

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simplify [3(2x-3y)]^2+[4(2x+3y)]^2

simplify

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

100 x^{2} + 84 x y + 225 y^{2}

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

Refine

= 9 (2 x - 3 y)^{2} + 16 (2 x + 3 y)^{2}

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

= 9 (4 x^{2} - 12 x y + 9 y^{2}) + 16 (2 x + 3 y)^{2}

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

= 9 (4 x^{2} - 12 x y + 9 y^{2}) + 16 (4 x^{2} + 12 x y + 9 y^{2})

Expand

9 (4 x^{2} - 12 x y + 9 y^{2}) : 36 x^{2} - 108 x y + 81 y^{2}

= 36 x^{2} - 108 x y + 81 y^{2} + 16 (4 x^{2} + 12 x y + 9 y^{2})

Expand

16 (4 x^{2} + 12 x y + 9 y^{2}) : 64 x^{2} + 192 x y + 144 y^{2}

= 36 x^{2} - 108 x y + 81 y^{2} + 64 x^{2} + 192 x y + 144 y^{2}

Simplify

36 x^{2} - 108 x y + 81 y^{2} + 64 x^{2} + 192 x y + 144 y^{2} : 100 x^{2} + 84 x y + 225 y^{2}

= 100 x^{2} + 84 x y + 225 y^{2}

(b^{2} - 2 b)^{3}

(2^{a} - 3 b)^{2}

\frac{2}{( x + 2 )} + \frac{5}{( x - 2 )}

(x^{2} - 5 y)^{3}

\frac{( 15 a - 12 b )}{( 6 a - 9 b )}

What is [3(2x-3y)]^2+[4(2x+3y)]^2 ?
The solution to [3(2x-3y)]^2+[4(2x+3y)]^2 is 100x^2+84xy+225y^2