Solve 4(a+b)(a-b)+(2a+2b-1)

$$4 ( a + b ) ( a - b ) + ( 2 a + 2 b - 1 )$$

Evaluate

$$4\left(a^{2}-b^{2}\right)+2a+2b-1$$

Solution Steps

Use the distributive property to multiply 4 by a+b.

$$\left(4a+4b\right)\left(a-b\right)+2a+2b-1$$

Apply the distributive property by multiplying each term of 4a+4b by each term of a-b.

$$4a^{2}-4ab+4ba-4b^{2}+2a+2b-1$$

Combine -4ab and 4ba to get 0.

$$4a^{2}-4b^{2}+2a+2b-1$$

Expand

$$4a^{2}+2a-4b^{2}+2b-1$$

Solution Steps

Use the distributive property to multiply 4 by a+b.

$$\left(4a+4b\right)\left(a-b\right)+2a+2b-1$$

Apply the distributive property by multiplying each term of 4a+4b by each term of a-b.

$$4a^{2}-4ab+4ba-4b^{2}+2a+2b-1$$

Combine -4ab and 4ba to get 0.

$$4a^{2}-4b^{2}+2a+2b-1$$