Solve (x+4)^2-2y(x-4)-(x+4)(y-x)

$$( x + 4 ) ^ { 2 } - 2 y ( x - 4 ) - ( x + 4 ) ( y - x )$$

Evaluate

$$2x^{2}-3xy+12x+4y+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16-2y\left(x-4\right)-\left(x+4\right)\left(y-x\right)$$

Use the distributive property to multiply x+4 by y-x.

$$x^{2}+8x+16-2y\left(x-4\right)-\left(xy-x^{2}+4y-4x\right)$$

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

$$x^{2}+8x+16-2y\left(x-4\right)-xy+x^{2}-4y+4x$$

Use the distributive property to multiply -2y by x-4.

$$x^{2}+8x+16-2yx+8y-xy+x^{2}-4y+4x$$

Combine -2yx and -xy to get -3yx.

$$x^{2}+8x+16-3yx+8y+x^{2}-4y+4x$$

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

$$2x^{2}+8x+16-3yx+8y-4y+4x$$

Combine 8y and -4y to get 4y.

$$2x^{2}+8x+16-3yx+4y+4x$$

Combine 8x and 4x to get 12x.

$$2x^{2}+12x+16-3yx+4y$$

Expand

$$2x^{2}-3xy+12x+4y+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$x^{2}+8x+16-2y\left(x-4\right)-\left(x+4\right)\left(y-x\right)$$

Use the distributive property to multiply x+4 by y-x.

$$x^{2}+8x+16-2y\left(x-4\right)-\left(xy-x^{2}+4y-4x\right)$$

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

$$x^{2}+8x+16-2y\left(x-4\right)-xy+x^{2}-4y+4x$$

Use the distributive property to multiply -2y by x-4.

$$x^{2}+8x+16-2yx+8y-xy+x^{2}-4y+4x$$

Combine -2yx and -xy to get -3yx.

$$x^{2}+8x+16-3yx+8y+x^{2}-4y+4x$$

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

$$2x^{2}+8x+16-3yx+8y-4y+4x$$

Combine 8y and -4y to get 4y.

$$2x^{2}+8x+16-3yx+4y+4x$$

Combine 8x and 4x to get 12x.

$$2x^{2}+12x+16-3yx+4y$$