Solve x+11^2-(x+2y)(x-2y)-(-2x)^2div(-4x)

$$x + 11 ^ { 2 } - ( x + 2 y ) ( x - 2 y ) - ( - 2 x ) ^ { 2 } \div ( - 4 x )$$

Evaluate

$$121+4y^{2}+2x-x^{2}$$

Solution Steps

Calculate 11 to the power of 2 and get 121.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{\left(-2x\right)^{2}}{-4x}$$

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

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{\left(-2\right)^{2}x^{2}}{-4x}$$

Calculate -2 to the power of 2 and get 4.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{4x^{2}}{-4x}$$

Cancel out 4x in both numerator and denominator.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{x}{-1}$$

Anything divided by -1 gives its opposite.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\left(-x\right)$$

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

$$x+121-\left(x^{2}-\left(2y\right)^{2}\right)-\left(-x\right)$$

Expand \left(2y\right)^{2}.

$$x+121-\left(x^{2}-2^{2}y^{2}\right)-\left(-x\right)$$

Calculate 2 to the power of 2 and get 4.

$$x+121-\left(x^{2}-4y^{2}\right)-\left(-x\right)$$

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

$$x+121-x^{2}+4y^{2}-\left(-x\right)$$

Multiply -1 and -1 to get 1.

$$x+121-x^{2}+4y^{2}+x$$

Combine x and x to get 2x.

$$2x+121-x^{2}+4y^{2}$$

Expand

$$121+4y^{2}+2x-x^{2}$$

Solution Steps

Calculate 11 to the power of 2 and get 121.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{\left(-2x\right)^{2}}{-4x}$$

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

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{\left(-2\right)^{2}x^{2}}{-4x}$$

Calculate -2 to the power of 2 and get 4.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{4x^{2}}{-4x}$$

Cancel out 4x in both numerator and denominator.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\frac{x}{-1}$$

Anything divided by -1 gives its opposite.

$$x+121-\left(x+2y\right)\left(x-2y\right)-\left(-x\right)$$

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

$$x+121-\left(x^{2}-\left(2y\right)^{2}\right)-\left(-x\right)$$

Expand \left(2y\right)^{2}.

$$x+121-\left(x^{2}-2^{2}y^{2}\right)-\left(-x\right)$$

Calculate 2 to the power of 2 and get 4.

$$x+121-\left(x^{2}-4y^{2}\right)-\left(-x\right)$$

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

$$x+121-x^{2}+4y^{2}-\left(-x\right)$$

Multiply -1 and -1 to get 1.

$$x+121-x^{2}+4y^{2}+x$$

Combine x and x to get 2x.

$$2x+121-x^{2}+4y^{2}$$