Resol (x^2+2xsqrt{x^2+24}+x^2+24)*(x^2-2xsqrt{{x}^2+24}+{x}^2+24)

$$( { x }^{ 2 } +2x \sqrt{ { x }^{ 2 } +24 } + { x }^{ 2 } +24) \times ( { x }^{ 2 } -2x \sqrt{ { x }^{ 2 } +24 } + { x }^{ 2 } +24)$$

Calcula

$$576$$

Passos de solució

Combineu x^{2} i x^{2} per obtenir 2x^{2}.

$$\left(2x^{2}+2x\sqrt{x^{2}+24}+24\right)\left(x^{2}-2x\sqrt{x^{2}+24}+x^{2}+24\right)$$

Utilitzeu la propietat distributiva per multiplicar 2x^{2}+2x\sqrt{x^{2}+24}+24 per x^{2}-2x\sqrt{x^{2}+24}+x^{2}+24 i combinar-los com termes.

$$2x^{2}\left(x^{2}-2x\sqrt{x^{2}+24}\right)+2x^{4}+72x^{2}+2x\sqrt{x^{2}+24}\left(x^{2}-2x\sqrt{x^{2}+24}\right)+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Utilitzeu la propietat distributiva per multiplicar 2x^{2} per x^{2}-2x\sqrt{x^{2}+24}.

$$2x^{4}-4\sqrt{x^{2}+24}x^{3}+2x^{4}+72x^{2}+2x\sqrt{x^{2}+24}\left(x^{2}-2x\sqrt{x^{2}+24}\right)+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Combineu 2x^{4} i 2x^{4} per obtenir 4x^{4}.

$$4x^{4}-4\sqrt{x^{2}+24}x^{3}+72x^{2}+2x\sqrt{x^{2}+24}\left(x^{2}-2x\sqrt{x^{2}+24}\right)+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Utilitzeu la propietat distributiva per multiplicar 2x\sqrt{x^{2}+24} per x^{2}-2x\sqrt{x^{2}+24}.

$$4x^{4}-4\sqrt{x^{2}+24}x^{3}+72x^{2}+2\sqrt{x^{2}+24}x^{3}-4\left(\sqrt{x^{2}+24}\right)^{2}x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Calculeu \sqrt{x^{2}+24} elevat a 2 per obtenir x^{2}+24.

$$4x^{4}-4\sqrt{x^{2}+24}x^{3}+72x^{2}+2\sqrt{x^{2}+24}x^{3}-4\left(x^{2}+24\right)x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Utilitzeu la propietat distributiva per multiplicar -4 per x^{2}+24.

$$4x^{4}-4\sqrt{x^{2}+24}x^{3}+72x^{2}+2\sqrt{x^{2}+24}x^{3}+\left(-4x^{2}-96\right)x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Utilitzeu la propietat distributiva per multiplicar -4x^{2}-96 per x^{2}.

$$4x^{4}-4\sqrt{x^{2}+24}x^{3}+72x^{2}+2\sqrt{x^{2}+24}x^{3}-4x^{4}-96x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Combineu -4\sqrt{x^{2}+24}x^{3} i 2\sqrt{x^{2}+24}x^{3} per obtenir -2\sqrt{x^{2}+24}x^{3}.

$$4x^{4}-2\sqrt{x^{2}+24}x^{3}+72x^{2}-4x^{4}-96x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Combineu 4x^{4} i -4x^{4} per obtenir 0.

$$-2\sqrt{x^{2}+24}x^{3}+72x^{2}-96x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Combineu 72x^{2} i -96x^{2} per obtenir -24x^{2}.

$$-2\sqrt{x^{2}+24}x^{3}-24x^{2}+2\sqrt{x^{2}+24}x^{3}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Combineu -2\sqrt{x^{2}+24}x^{3} i 2\sqrt{x^{2}+24}x^{3} per obtenir 0.

$$-24x^{2}+48\sqrt{x^{2}+24}x+24\left(x^{2}-2x\sqrt{x^{2}+24}\right)+576$$

Utilitzeu la propietat distributiva per multiplicar 24 per x^{2}-2x\sqrt{x^{2}+24}.

$$-24x^{2}+48\sqrt{x^{2}+24}x+24x^{2}-48\sqrt{x^{2}+24}x+576$$

Combineu -24x^{2} i 24x^{2} per obtenir 0.

$$48\sqrt{x^{2}+24}x-48\sqrt{x^{2}+24}x+576$$

Combineu 48\sqrt{x^{2}+24}x i -48\sqrt{x^{2}+24}x per obtenir 0.

$$576$$

Factoritzar

$$2^{6}\times 3^{2}$$