Question

a²-b²- 2a + 1 and a ²-ab-a​

Answer 1

The idea is to just expand the formulae.

We know

[math](a+b)^2 = a^2+b^2+2ab[/math]

[math](a-b)^2 = a^2+b^2-2ab[/math]

So,

[math]\dfrac{1}{2}[ (a+b)^2 + (a-b)^2 ][/math]

[math]= \dfrac{1}{2}[ (a^2+b^2+2ab )+(a^2+b^2-2ab ) ][/math]

Cancelling [math]\hspace{1mm} +2ab \hspace{1mm} [/math]and[math] \hspace{1mm} -2ab \hspace{1mm} [/math] and adding like terms [math]\text{ } a^2 \text{ and } b^2[/math],

[math]= \dfrac{1}{2}[ 2a^2+2b^2][/math]

Taking 2 as common from [math]\hspace{1mm} a^2 \text{ and } b^2[/math],

[math]= \dfrac{1}{2}[ 2(a^2+b^2) ][/math]

Cancelling the 2,

[math]= \boxed{a^2+b^2}[/math]