Solve (2x+5e)(3x+4e)-(7x+2e)(2x+1e)

$$(2x+5e)(3x+4e)-(7x+2e)(2x+1e)$$

Evaluate

$$18e^{2}+12ex-8x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+5e by each term of 3x+4e.

$$6x^{2}+8ex+15ex+20e^{2}-\left(7x+2e\right)\left(2x+1e\right)$$

Combine 8ex and 15ex to get 23ex.

$$6x^{2}+23ex+20e^{2}-\left(7x+2e\right)\left(2x+1e\right)$$

Apply the distributive property by multiplying each term of 7x+2e by each term of 2x+1e.

$$6x^{2}+23ex+20e^{2}-\left(14x^{2}+7xe+4ex+2e^{2}\right)$$

Combine 7xe and 4ex to get 11xe.

$$6x^{2}+23ex+20e^{2}-\left(14x^{2}+11xe+2e^{2}\right)$$

To find the opposite of 14x^{2}+11xe+2e^{2}, find the opposite of each term.

$$6x^{2}+23ex+20e^{2}-14x^{2}-11xe-2e^{2}$$

Combine 6x^{2} and -14x^{2} to get -8x^{2}.

$$-8x^{2}+23ex+20e^{2}-11xe-2e^{2}$$

Combine 23ex and -11xe to get 12ex.

$$-8x^{2}+12ex+20e^{2}-2e^{2}$$

Combine 20e^{2} and -2e^{2} to get 18e^{2}.

$$-8x^{2}+12ex+18e^{2}$$

Expand

$$18e^{2}+12ex-8x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+5e by each term of 3x+4e.

$$6x^{2}+8ex+15ex+20e^{2}-\left(7x+2e\right)\left(2x+1e\right)$$

Combine 8ex and 15ex to get 23ex.

$$6x^{2}+23ex+20e^{2}-\left(7x+2e\right)\left(2x+1e\right)$$

Apply the distributive property by multiplying each term of 7x+2e by each term of 2x+1e.

$$6x^{2}+23ex+20e^{2}-\left(14x^{2}+7xe+4ex+2e^{2}\right)$$

Combine 7xe and 4ex to get 11xe.

$$6x^{2}+23ex+20e^{2}-\left(14x^{2}+11xe+2e^{2}\right)$$

To find the opposite of 14x^{2}+11xe+2e^{2}, find the opposite of each term.

$$6x^{2}+23ex+20e^{2}-14x^{2}-11xe-2e^{2}$$

Combine 6x^{2} and -14x^{2} to get -8x^{2}.

$$-8x^{2}+23ex+20e^{2}-11xe-2e^{2}$$

Combine 23ex and -11xe to get 12ex.

$$-8x^{2}+12ex+20e^{2}-2e^{2}$$

Combine 20e^{2} and -2e^{2} to get 18e^{2}.

$$-8x^{2}+12ex+18e^{2}$$