Solve left(2020x+2019right)^2+left(2020x+2020right)^2+left(2020x+2021right)^2*(2020x

$${ \left(2020x+2019 \right) }^{ 2 } + { \left(2020x+2020 \right) }^{ 2 } + { \left(2020x+2021 \right) }^{ 2 } \times (2020x$$

Evaluate

$$8242408000x^{3}[phone]x^{2}[phone]x+8156761$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2019\right)^{2}.

$$4080400x^{2}+8156760x+4076361+\left(2020x+2020\right)^{2}+\left(2020x+2021\right)^{2}\times 2020x$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2020\right)^{2}.

$$4080400x^{2}+8156760x+4076361+4080400x^{2}+8160800x+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Combine 4080400x^{2} and 4080400x^{2} to get 8160800x^{2}.

$$8160800x^{2}+8156760x+4076361+8160800x+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Combine 8156760x and 8160800x to get 16317560x.

$$8160800x^{2}[phone]x+4076361+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Add 4076361 and 4080400 to get 8156761.

$$8160800x^{2}[phone]x+8156761+\left(2020x+2021\right)^{2}\times 2020x$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2021\right)^{2}.

$$8160800x^{2}[phone]x+8156761+\left(4080400x^{2}+8164840x+4084441\right)\times 2020x$$

Use the distributive property to multiply 4080400x^{2}+8164840x+4084441 by 2020.

$$8160800x^{2}[phone]x+8156761+\left(8242408000x^{2}[phone]x+8250570820\right)x$$

Use the distributive property to multiply 8242408000x^{2}[phone]x+8250570820 by x.

$$8160800x^{2}[phone]x+8156761+8242408000x^{3}[phone]x^{2}[phone]x$$

Combine 8160800x^{2} and 16492976800x^{2} to get 16501137600x^{2}.

$$16501137600x^{2}[phone]x+8156761+8242408000x^{3}[phone]x$$

Combine 16317560x and 8250570820x to get 8266888380x.

$$16501137600x^{2}[phone]x+8156761+8242408000x^{3}$$

Expand

$$8242408000x^{3}[phone]x^{2}[phone]x+8156761$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2019\right)^{2}.

$$4080400x^{2}+8156760x+4076361+\left(2020x+2020\right)^{2}+\left(2020x+2021\right)^{2}\times 2020x$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2020\right)^{2}.

$$4080400x^{2}+8156760x+4076361+4080400x^{2}+8160800x+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Combine 4080400x^{2} and 4080400x^{2} to get 8160800x^{2}.

$$8160800x^{2}+8156760x+4076361+8160800x+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Combine 8156760x and 8160800x to get 16317560x.

$$8160800x^{2}[phone]x+4076361+4080400+\left(2020x+2021\right)^{2}\times 2020x$$

Add 4076361 and 4080400 to get 8156761.

$$8160800x^{2}[phone]x+8156761+\left(2020x+2021\right)^{2}\times 2020x$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2020x+2021\right)^{2}.

$$8160800x^{2}[phone]x+8156761+\left(4080400x^{2}+8164840x+4084441\right)\times 2020x$$

Use the distributive property to multiply 4080400x^{2}+8164840x+4084441 by 2020.

$$8160800x^{2}[phone]x+8156761+\left(8242408000x^{2}[phone]x+8250570820\right)x$$

Use the distributive property to multiply 8242408000x^{2}[phone]x+8250570820 by x.

$$8160800x^{2}[phone]x+8156761+8242408000x^{3}[phone]x^{2}[phone]x$$

Combine 8160800x^{2} and 16492976800x^{2} to get 16501137600x^{2}.

$$16501137600x^{2}[phone]x+8156761+8242408000x^{3}[phone]x$$

Combine 16317560x and 8250570820x to get 8266888380x.

$$16501137600x^{2}[phone]x+8156761+8242408000x^{3}$$