Solve (a+b-n)*(a+b+n)

$$( a + b - n ) \cdot ( a + b + n )$$

Evaluate

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

Solution Steps

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

$$a^{2}+ab+an+ba+b^{2}+bn-na-nb-n^{2}$$

Combine ab and ba to get 2ab.

$$a^{2}+2ab+an+b^{2}+bn-na-nb-n^{2}$$

Combine an and -na to get 0.

$$a^{2}+2ab+b^{2}+bn-nb-n^{2}$$

Combine bn and -nb to get 0.

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

Expand

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

Solution Steps

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

$$a^{2}+ab+an+ba+b^{2}+bn-na-nb-n^{2}$$

Combine ab and ba to get 2ab.

$$a^{2}+2ab+an+b^{2}+bn-na-nb-n^{2}$$

Combine an and -na to get 0.

$$a^{2}+2ab+b^{2}+bn-nb-n^{2}$$

Combine bn and -nb to get 0.

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