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

$$( 2 a + b ) ( a - b + 1 ) + b ( b - 1 )$$

Evaluate

$$a\left(2a-b+2\right)$$

Solution Steps

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

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

Combine -2ab and ba to get -ab.

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

Use the distributive property to multiply b by b-1.

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

Combine -b^{2} and b^{2} to get 0.

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

Combine b and -b to get 0.

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

Expand

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

Solution Steps

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

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

Combine -2ab and ba to get -ab.

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

Use the distributive property to multiply b by b-1.

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

Combine -b^{2} and b^{2} to get 0.

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

Combine b and -b to get 0.

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