Solve (2a+b)*(-3a+b+1)-(a+b)*(a-b-1)

$$( 2 a + b ) \cdot ( - 3 a + b + 1 ) - ( a + b ) \cdot ( a - b - 1 )$$

Evaluate

$$2b+2b^{2}+3a-ab-7a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2a+b by each term of -3a+b+1.

$$-6a^{2}+2ab+2a-3ba+b^{2}+b-\left(a+b\right)\left(a-b-1\right)$$

Combine 2ab and -3ba to get -ab.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a+b\right)\left(a-b-1\right)$$

Apply the distributive property by multiplying each term of a+b by each term of a-b-1.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a^{2}-ab-a+ba-b^{2}-b\right)$$

Combine -ab and ba to get 0.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a^{2}-a-b^{2}-b\right)$$

To find the opposite of a^{2}-a-b^{2}-b, find the opposite of each term.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}-\left(-a\right)-\left(-b^{2}\right)-\left(-b\right)$$

The opposite of -a is a.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a-\left(-b^{2}\right)-\left(-b\right)$$

The opposite of -b^{2} is b^{2}.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a+b^{2}-\left(-b\right)$$

The opposite of -b is b.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a+b^{2}+b$$

Combine -6a^{2} and -a^{2} to get -7a^{2}.

$$-7a^{2}-ab+2a+b^{2}+b+a+b^{2}+b$$

Combine 2a and a to get 3a.

$$-7a^{2}-ab+3a+b^{2}+b+b^{2}+b$$

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

$$-7a^{2}-ab+3a+2b^{2}+b+b$$

Combine b and b to get 2b.

$$-7a^{2}-ab+3a+2b^{2}+2b$$

Expand

$$2b+2b^{2}+3a-ab-7a^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2a+b by each term of -3a+b+1.

$$-6a^{2}+2ab+2a-3ba+b^{2}+b-\left(a+b\right)\left(a-b-1\right)$$

Combine 2ab and -3ba to get -ab.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a+b\right)\left(a-b-1\right)$$

Apply the distributive property by multiplying each term of a+b by each term of a-b-1.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a^{2}-ab-a+ba-b^{2}-b\right)$$

Combine -ab and ba to get 0.

$$-6a^{2}-ab+2a+b^{2}+b-\left(a^{2}-a-b^{2}-b\right)$$

To find the opposite of a^{2}-a-b^{2}-b, find the opposite of each term.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}-\left(-a\right)-\left(-b^{2}\right)-\left(-b\right)$$

The opposite of -a is a.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a-\left(-b^{2}\right)-\left(-b\right)$$

The opposite of -b^{2} is b^{2}.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a+b^{2}-\left(-b\right)$$

The opposite of -b is b.

$$-6a^{2}-ab+2a+b^{2}+b-a^{2}+a+b^{2}+b$$

Combine -6a^{2} and -a^{2} to get -7a^{2}.

$$-7a^{2}-ab+2a+b^{2}+b+a+b^{2}+b$$

Combine 2a and a to get 3a.

$$-7a^{2}-ab+3a+b^{2}+b+b^{2}+b$$

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

$$-7a^{2}-ab+3a+2b^{2}+b+b$$

Combine b and b to get 2b.

$$-7a^{2}-ab+3a+2b^{2}+2b$$