Solve left(2x+5yright)left(2x-5yright)+left(2x+yright)left(-2x-yright)

$$\left( 2x+5y \right) \left( 2x-5y \right) + \left( 2x+y \right) \left( -2x-y \right)$$

Evaluate

$$-2y\left(2x+13y\right)$$

Solution Steps

Consider \left(2x+5y\right)\left(2x-5y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand \left(5y\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

$$4x^{2}-25y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

Apply the distributive property by multiplying each term of 2x+y by each term of -2x-y.

$$4x^{2}-25y^{2}-4x^{2}-2xy-2yx-y^{2}$$

Combine -2xy and -2yx to get -4xy.

$$4x^{2}-25y^{2}-4x^{2}-4xy-y^{2}$$

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

$$-25y^{2}-4xy-y^{2}$$

Combine -25y^{2} and -y^{2} to get -26y^{2}.

$$-26y^{2}-4xy$$

Expand

$$-4xy-26y^{2}$$

Solution Steps

Consider \left(2x+5y\right)\left(2x-5y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand \left(5y\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

$$4x^{2}-25y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

Apply the distributive property by multiplying each term of 2x+y by each term of -2x-y.

$$4x^{2}-25y^{2}-4x^{2}-2xy-2yx-y^{2}$$

Combine -2xy and -2yx to get -4xy.

$$4x^{2}-25y^{2}-4x^{2}-4xy-y^{2}$$

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

$$-25y^{2}-4xy-y^{2}$$

Combine -25y^{2} and -y^{2} to get -26y^{2}.

$$-26y^{2}-4xy$$