Solve 5(2x+5y)(2x-5y)+(2x+y)(-2x-y)

$$5 ( 2 x + 5 y ) ( 2 x - 5 y ) + ( 2 x + y ) ( - 2 x - y )$$

Evaluate

$$16x^{2}-4xy-126y^{2}$$

Solution Steps

Use the distributive property to multiply 5 by 2x+5y.

$$\left(10x+25y\right)\left(2x-5y\right)+\left(2x+y\right)\left(-2x-y\right)$$

Apply the distributive property by multiplying each term of 10x+25y by each term of 2x-5y.

$$20x^{2}-50xy+50yx-125y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

Combine -50xy and 50yx to get 0.

$$20x^{2}-125y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

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

$$20x^{2}-125y^{2}-4x^{2}-2xy-2yx-y^{2}$$

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

$$20x^{2}-125y^{2}-4x^{2}-4xy-y^{2}$$

Combine 20x^{2} and -4x^{2} to get 16x^{2}.

$$16x^{2}-125y^{2}-4xy-y^{2}$$

Combine -125y^{2} and -y^{2} to get -126y^{2}.

$$16x^{2}-126y^{2}-4xy$$

Expand

$$16x^{2}-4xy-126y^{2}$$

Solution Steps

Use the distributive property to multiply 5 by 2x+5y.

$$\left(10x+25y\right)\left(2x-5y\right)+\left(2x+y\right)\left(-2x-y\right)$$

Apply the distributive property by multiplying each term of 10x+25y by each term of 2x-5y.

$$20x^{2}-50xy+50yx-125y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

Combine -50xy and 50yx to get 0.

$$20x^{2}-125y^{2}+\left(2x+y\right)\left(-2x-y\right)$$

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

$$20x^{2}-125y^{2}-4x^{2}-2xy-2yx-y^{2}$$

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

$$20x^{2}-125y^{2}-4x^{2}-4xy-y^{2}$$

Combine 20x^{2} and -4x^{2} to get 16x^{2}.

$$16x^{2}-125y^{2}-4xy-y^{2}$$

Combine -125y^{2} and -y^{2} to get -126y^{2}.

$$16x^{2}-126y^{2}-4xy$$