Solve (a-b+3)(a-b-3)

$$( a - b + 3 ) ( a - b - 3 )$$

Evaluate

$$\left(a-b\right)^{2}-9$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=a-b and b=3.

$$\left(a-b\right)^{2}-3^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$a^{2}-2ab+b^{2}-9$$

Expand

$$a^{2}-2ab+b^{2}-9$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=a-b and b=3.

$$\left(a-b\right)^{2}-3^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$a^{2}-2ab+b^{2}-9$$