Solve (x-a)(x+a)-(x-2a)^2

$$( x - a ) ( x + a ) - ( x - 2 a ) ^ { 2 }$$

Evaluate

$$a\left(4x-5a\right)$$

Solution Steps

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

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

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

$$x^{2}-a^{2}-\left(x^{2}-4xa+4a^{2}\right)$$

To find the opposite of x^{2}-4xa+4a^{2}, find the opposite of each term.

$$x^{2}-a^{2}-x^{2}+4xa-4a^{2}$$

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

$$-a^{2}+4xa-4a^{2}$$

Combine -a^{2} and -4a^{2} to get -5a^{2}.

$$-5a^{2}+4xa$$

Expand

$$4ax-5a^{2}$$

Solution Steps

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

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

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

$$x^{2}-a^{2}-\left(x^{2}-4xa+4a^{2}\right)$$

To find the opposite of x^{2}-4xa+4a^{2}, find the opposite of each term.

$$x^{2}-a^{2}-x^{2}+4xa-4a^{2}$$

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

$$-a^{2}+4xa-4a^{2}$$

Combine -a^{2} and -4a^{2} to get -5a^{2}.

$$-5a^{2}+4xa$$