Solve (x+2y)^2-(3x-y)(x-4y)]div2x

$$( x + 2 y ) ^ { 2 } - ( 3 x - y ) ( x - 4 y ) ] \div 2 x$$

Evaluate

$$x\left(17y-2x\right)$$

Solution Steps

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

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

Use the distributive property to multiply 3x-y by x-4y and combine like terms.

$$x^{2}+4xy+4y^{2}-\left(3x^{2}-13xy+4y^{2}\right)$$

To find the opposite of 3x^{2}-13xy+4y^{2}, find the opposite of each term.

$$x^{2}+4xy+4y^{2}-3x^{2}+13xy-4y^{2}$$

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

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

Combine 4xy and 13xy to get 17xy.

$$-2x^{2}+17xy+4y^{2}-4y^{2}$$

Combine 4y^{2} and -4y^{2} to get 0.

$$-2x^{2}+17xy$$

Expand

$$17xy-2x^{2}$$

Solution Steps

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

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

Use the distributive property to multiply 3x-y by x-4y and combine like terms.

$$x^{2}+4xy+4y^{2}-\left(3x^{2}-13xy+4y^{2}\right)$$

To find the opposite of 3x^{2}-13xy+4y^{2}, find the opposite of each term.

$$x^{2}+4xy+4y^{2}-3x^{2}+13xy-4y^{2}$$

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

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

Combine 4xy and 13xy to get 17xy.

$$-2x^{2}+17xy+4y^{2}-4y^{2}$$

Combine 4y^{2} and -4y^{2} to get 0.

$$-2x^{2}+17xy$$