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

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

Multiply 5 and 2 to get 10.

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 10 and 8 to get 80.

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

Calculate 5 to the power of 2 and get 25.

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

Multiply 80 and 25 to get 2000.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 10 and 4 to get 40.

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

Calculate 5 to the power of 3 and get 125.

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

Multiply 40 and 125 to get 5000.

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

Calculate 5 to the power of 5 and get 3125.

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

Multiply 3125 and 2 to get 6250.

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

Combine -10x and 6250x to get 6240x.

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

Calculate 5 to the power of 5 and get 3125.

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

Subtract 3125 from 5 to get -3120.

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

Expand

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

Multiply 5 and 2 to get 10.

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 10 and 8 to get 80.

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

Calculate 5 to the power of 2 and get 25.

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

Multiply 80 and 25 to get 2000.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 10 and 4 to get 40.

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

Calculate 5 to the power of 3 and get 125.

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

Multiply 40 and 125 to get 5000.

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

Calculate 5 to the power of 5 and get 3125.

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

Multiply 3125 and 2 to get 6250.

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

Combine -10x and 6250x to get 6240x.

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

Calculate 5 to the power of 5 and get 3125.

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

Subtract 3125 from 5 to get -3120.

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