Resol y^5-5*2x+5+10left(2xright)^35^2-10left(2xright)^2{5}^3+5*2x{5}^4-{5}^5

$${ y }^{ 5 } -5 \cdot 2x+5+10 { \left(2x \right) }^{ 3 } { 5 }^{ 2 } -10 { \left(2x \right) }^{ 2 } { 5 }^{ 3 } +5 \cdot 2x { 5 }^{ 4 } - { 5 }^{ 5 }$$

Calcula

$$2000x^{3}-5000x^{2}+6240x+y^{5}-3120$$

Passos de solució

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu 1 i 4 per obtenir 5.

$$y^{5}-5\times 2x+5+10\times \left(2x\right)^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 5 per 2 per obtenir 10.

$$y^{5}-10x+5+10\times \left(2x\right)^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Expandiu \left(2x\right)^{3}.

$$y^{5}-10x+5+10\times 2^{3}x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 2 elevat a 3 per obtenir 8.

$$y^{5}-10x+5+10\times 8x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 10 per 8 per obtenir 80.

$$y^{5}-10x+5+80x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 2 per obtenir 25.

$$y^{5}-10x+5+80x^{3}\times 25-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 80 per 25 per obtenir 2000.

$$y^{5}-10x+5+2000x^{3}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Expandiu \left(2x\right)^{2}.

$$y^{5}-10x+5+2000x^{3}-10\times 2^{2}x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 2 elevat a 2 per obtenir 4.

$$y^{5}-10x+5+2000x^{3}-10\times 4x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 10 per 4 per obtenir 40.

$$y^{5}-10x+5+2000x^{3}-40x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 3 per obtenir 125.

$$y^{5}-10x+5+2000x^{3}-40x^{2}\times 125+5^{5}\times 2x-5^{5}$$

Multipliqueu 40 per 125 per obtenir 5000.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 5 per obtenir 3125.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+3125\times 2x-5^{5}$$

Multipliqueu 3125 per 2 per obtenir 6250.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+6250x-5^{5}$$

Combineu -10x i 6250x per obtenir 6240x.

$$y^{5}+6240x+5+2000x^{3}-5000x^{2}-5^{5}$$

Calculeu 5 elevat a 5 per obtenir 3125.

$$y^{5}+6240x+5+2000x^{3}-5000x^{2}-3125$$

Resteu 5 de 3125 per obtenir -3120.

$$y^{5}+6240x-3120+2000x^{3}-5000x^{2}$$

Expandiu

$$2000x^{3}-5000x^{2}+6240x+y^{5}-3120$$

Passos de solució

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu 1 i 4 per obtenir 5.

$$y^{5}-5\times 2x+5+10\times \left(2x\right)^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 5 per 2 per obtenir 10.

$$y^{5}-10x+5+10\times \left(2x\right)^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Expandiu \left(2x\right)^{3}.

$$y^{5}-10x+5+10\times 2^{3}x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 2 elevat a 3 per obtenir 8.

$$y^{5}-10x+5+10\times 8x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 10 per 8 per obtenir 80.

$$y^{5}-10x+5+80x^{3}\times 5^{2}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 2 per obtenir 25.

$$y^{5}-10x+5+80x^{3}\times 25-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 80 per 25 per obtenir 2000.

$$y^{5}-10x+5+2000x^{3}-10\times \left(2x\right)^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Expandiu \left(2x\right)^{2}.

$$y^{5}-10x+5+2000x^{3}-10\times 2^{2}x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 2 elevat a 2 per obtenir 4.

$$y^{5}-10x+5+2000x^{3}-10\times 4x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Multipliqueu 10 per 4 per obtenir 40.

$$y^{5}-10x+5+2000x^{3}-40x^{2}\times 5^{3}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 3 per obtenir 125.

$$y^{5}-10x+5+2000x^{3}-40x^{2}\times 125+5^{5}\times 2x-5^{5}$$

Multipliqueu 40 per 125 per obtenir 5000.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+5^{5}\times 2x-5^{5}$$

Calculeu 5 elevat a 5 per obtenir 3125.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+3125\times 2x-5^{5}$$

Multipliqueu 3125 per 2 per obtenir 6250.

$$y^{5}-10x+5+2000x^{3}-5000x^{2}+6250x-5^{5}$$

Combineu -10x i 6250x per obtenir 6240x.

$$y^{5}+6240x+5+2000x^{3}-5000x^{2}-5^{5}$$

Calculeu 5 elevat a 5 per obtenir 3125.

$$y^{5}+6240x+5+2000x^{3}-5000x^{2}-3125$$

Resteu 5 de 3125 per obtenir -3120.

$$y^{5}+6240x-3120+2000x^{3}-5000x^{2}$$