Solve 2left(y+3xright)^2+2y^2+5x+y+x+y^2+y^2

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

Evaluate

$$2\left(3x+y\right)^{2}+4y^{2}+y+6x$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3x\right)^{2}.

$$2\left(y^{2}+6yx+9x^{2}\right)+2y^{2}+5x+y+x+y^{2}+y^{2}$$

Use the distributive property to multiply 2 by y^{2}+6yx+9x^{2}.

$$2y^{2}+12yx+18x^{2}+2y^{2}+5x+y+x+y^{2}+y^{2}$$

Combine 2y^{2} and 2y^{2} to get 4y^{2}.

$$4y^{2}+12yx+18x^{2}+5x+y+x+y^{2}+y^{2}$$

Combine 5x and x to get 6x.

$$4y^{2}+12yx+18x^{2}+6x+y+y^{2}+y^{2}$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$5y^{2}+12yx+18x^{2}+6x+y+y^{2}$$

Combine 5y^{2} and y^{2} to get 6y^{2}.

$$6y^{2}+12yx+18x^{2}+6x+y$$

Expand

$$18x^{2}+12xy+6x+6y^{2}+y$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+3x\right)^{2}.

$$2\left(y^{2}+6yx+9x^{2}\right)+2y^{2}+5x+y+x+y^{2}+y^{2}$$

Use the distributive property to multiply 2 by y^{2}+6yx+9x^{2}.

$$2y^{2}+12yx+18x^{2}+2y^{2}+5x+y+x+y^{2}+y^{2}$$

Combine 2y^{2} and 2y^{2} to get 4y^{2}.

$$4y^{2}+12yx+18x^{2}+5x+y+x+y^{2}+y^{2}$$

Combine 5x and x to get 6x.

$$4y^{2}+12yx+18x^{2}+6x+y+y^{2}+y^{2}$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$5y^{2}+12yx+18x^{2}+6x+y+y^{2}$$

Combine 5y^{2} and y^{2} to get 6y^{2}.

$$6y^{2}+12yx+18x^{2}+6x+y$$