Solve (x-1)^2+(x-4)(x+4)-2x(x+2y)

$$( x - 1 ) ^ { 2 } + ( x - 4 ) ( x + 4 ) - 2 x ( x + 2 y )$$

Evaluate

$$-4xy-2x-15$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1+\left(x-4\right)\left(x+4\right)-2x\left(x+2y\right)$$

Consider \left(x-4\right)\left(x+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$x^{2}-2x+1+x^{2}-16-2x\left(x+2y\right)$$

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

$$2x^{2}-2x+1-16-2x\left(x+2y\right)$$

Subtract 16 from 1 to get -15.

$$2x^{2}-2x-15-2x\left(x+2y\right)$$

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

$$2x^{2}-2x-15-2x^{2}-4xy$$

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

$$-2x-15-4xy$$

Expand

$$-4xy-2x-15$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$x^{2}-2x+1+\left(x-4\right)\left(x+4\right)-2x\left(x+2y\right)$$

Consider \left(x-4\right)\left(x+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$x^{2}-2x+1+x^{2}-16-2x\left(x+2y\right)$$

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

$$2x^{2}-2x+1-16-2x\left(x+2y\right)$$

Subtract 16 from 1 to get -15.

$$2x^{2}-2x-15-2x\left(x+2y\right)$$

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

$$2x^{2}-2x-15-2x^{2}-4xy$$

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

$$-2x-15-4xy$$