Solve (2x-y)^2+(y+3x)(3x-y)+xy

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

Evaluate

$$x\left(13x-3y\right)$$

Solution Steps

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

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

Consider \left(y+3x\right)\left(3x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$4x^{2}-4xy+y^{2}+3^{2}x^{2}-y^{2}+xy$$

Calculate 3 to the power of 2 and get 9.

$$4x^{2}-4xy+y^{2}+9x^{2}-y^{2}+xy$$

Combine 4x^{2} and 9x^{2} to get 13x^{2}.

$$13x^{2}-4xy+y^{2}-y^{2}+xy$$

Combine y^{2} and -y^{2} to get 0.

$$13x^{2}-4xy+xy$$

Combine -4xy and xy to get -3xy.

$$13x^{2}-3xy$$

Expand

$$13x^{2}-3xy$$

Solution Steps

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

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

Consider \left(y+3x\right)\left(3x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$4x^{2}-4xy+y^{2}+3^{2}x^{2}-y^{2}+xy$$

Calculate 3 to the power of 2 and get 9.

$$4x^{2}-4xy+y^{2}+9x^{2}-y^{2}+xy$$

Combine 4x^{2} and 9x^{2} to get 13x^{2}.

$$13x^{2}-4xy+y^{2}-y^{2}+xy$$

Combine y^{2} and -y^{2} to get 0.

$$13x^{2}-4xy+xy$$

Combine -4xy and xy to get -3xy.

$$13x^{2}-3xy$$