Resol 25left(x-yright)^2-9left(x+yright)^2

$$25 { \left(x-y \right) }^{ 2 } -9 { \left(x+y \right) }^{ 2 }$$

Calcula

$$4\left(x-4y\right)\left(4x-y\right)$$

Passos de solució

Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-y\right)^{2}.

$$25\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)^{2}$$

Utilitzeu la propietat distributiva per multiplicar 25 per x^{2}-2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(x+y\right)^{2}.

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

Utilitzeu la propietat distributiva per multiplicar -9 per x^{2}+2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

Combineu 25x^{2} i -9x^{2} per obtenir 16x^{2}.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

Combineu -50xy i -18xy per obtenir -68xy.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

Combineu 25y^{2} i -9y^{2} per obtenir 16y^{2}.

$$16x^{2}-68xy+16y^{2}$$

Expandiu

$$16x^{2}-68xy+16y^{2}$$

Passos de solució

Utilitzeu el teorema del binomi \left(a-b\right)^{2}=a^{2}-2ab+b^{2} per desenvolupar \left(x-y\right)^{2}.

$$25\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)^{2}$$

Utilitzeu la propietat distributiva per multiplicar 25 per x^{2}-2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9\left(x+y\right)^{2}$$

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(x+y\right)^{2}.

$$25x^{2}-50xy+25y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

Utilitzeu la propietat distributiva per multiplicar -9 per x^{2}+2xy+y^{2}.

$$25x^{2}-50xy+25y^{2}-9x^{2}-18xy-9y^{2}$$

Combineu 25x^{2} i -9x^{2} per obtenir 16x^{2}.

$$16x^{2}-50xy+25y^{2}-18xy-9y^{2}$$

Combineu -50xy i -18xy per obtenir -68xy.

$$16x^{2}-68xy+25y^{2}-9y^{2}$$

Combineu 25y^{2} i -9y^{2} per obtenir 16y^{2}.

$$16x^{2}-68xy+16y^{2}$$