Solve x^2+(x+y)1^2+(x+2y)1^2+(x+3y)1^2

$${ x }^{ 2 } +(x+y) { 1 }^{ 2 } +(x+2y) { 1 }^{ 2 } +(x+3y) { 1 }^{ 2 }$$

Evaluate

$$x^{2}+3x+6y$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$x^{2}+\left(x+y\right)\times 1+\left(x+2y\right)\times 1^{2}+\left(x+3y\right)\times 1^{2}$$

Use the distributive property to multiply x+y by 1.

$$x^{2}+x+y+\left(x+2y\right)\times 1^{2}+\left(x+3y\right)\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+x+y+\left(x+2y\right)\times 1+\left(x+3y\right)\times 1^{2}$$

Use the distributive property to multiply x+2y by 1.

$$x^{2}+x+y+x+2y+\left(x+3y\right)\times 1^{2}$$

Combine x and x to get 2x.

$$x^{2}+2x+y+2y+\left(x+3y\right)\times 1^{2}$$

Combine y and 2y to get 3y.

$$x^{2}+2x+3y+\left(x+3y\right)\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+2x+3y+\left(x+3y\right)\times 1$$

Use the distributive property to multiply x+3y by 1.

$$x^{2}+2x+3y+x+3y$$

Combine 2x and x to get 3x.

$$x^{2}+3x+3y+3y$$

Combine 3y and 3y to get 6y.

$$x^{2}+3x+6y$$

Expand

$$x^{2}+3x+6y$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$x^{2}+\left(x+y\right)\times 1+\left(x+2y\right)\times 1^{2}+\left(x+3y\right)\times 1^{2}$$

Use the distributive property to multiply x+y by 1.

$$x^{2}+x+y+\left(x+2y\right)\times 1^{2}+\left(x+3y\right)\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+x+y+\left(x+2y\right)\times 1+\left(x+3y\right)\times 1^{2}$$

Use the distributive property to multiply x+2y by 1.

$$x^{2}+x+y+x+2y+\left(x+3y\right)\times 1^{2}$$

Combine x and x to get 2x.

$$x^{2}+2x+y+2y+\left(x+3y\right)\times 1^{2}$$

Combine y and 2y to get 3y.

$$x^{2}+2x+3y+\left(x+3y\right)\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+2x+3y+\left(x+3y\right)\times 1$$

Use the distributive property to multiply x+3y by 1.

$$x^{2}+2x+3y+x+3y$$

Combine 2x and x to get 3x.

$$x^{2}+3x+3y+3y$$

Combine 3y and 3y to get 6y.

$$x^{2}+3x+6y$$