Solve 3(2x-y)^2+2y(2x-y)-5y^2

$$3 ( 2 x - y ) ^ { 2 } + 2 y ( 2 x - y ) - 5 y ^ { 2 }$$

Evaluate

$$4\left(x-y\right)\left(3x+y\right)$$

Solution Steps

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

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

Use the distributive property to multiply 3 by 4x^{2}-4xy+y^{2}.

$$12x^{2}-12xy+3y^{2}+2y\left(2x-y\right)-5y^{2}$$

Use the distributive property to multiply 2y by 2x-y.

$$12x^{2}-12xy+3y^{2}+4yx-2y^{2}-5y^{2}$$

Combine -12xy and 4yx to get -8xy.

$$12x^{2}-8xy+3y^{2}-2y^{2}-5y^{2}$$

Combine 3y^{2} and -2y^{2} to get y^{2}.

$$12x^{2}-8xy+y^{2}-5y^{2}$$

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

$$12x^{2}-8xy-4y^{2}$$

Expand

$$12x^{2}-8xy-4y^{2}$$

Solution Steps

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

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

Use the distributive property to multiply 3 by 4x^{2}-4xy+y^{2}.

$$12x^{2}-12xy+3y^{2}+2y\left(2x-y\right)-5y^{2}$$

Use the distributive property to multiply 2y by 2x-y.

$$12x^{2}-12xy+3y^{2}+4yx-2y^{2}-5y^{2}$$

Combine -12xy and 4yx to get -8xy.

$$12x^{2}-8xy+3y^{2}-2y^{2}-5y^{2}$$

Combine 3y^{2} and -2y^{2} to get y^{2}.

$$12x^{2}-8xy+y^{2}-5y^{2}$$

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

$$12x^{2}-8xy-4y^{2}$$