Solve (x+a-1)(x+a+1)

$$( x + a - 1 ) ( x + a + 1 )$$

Evaluate

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

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=x+a and b=1.

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

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

$$x^{2}+2xa+a^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+2xa+a^{2}-1$$

Expand

$$x^{2}+2ax+a^{2}-1$$

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=x+a and b=1.

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

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

$$x^{2}+2xa+a^{2}-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x^{2}+2xa+a^{2}-1$$