Question

Match the following identities:

• A. $a^2-9$
• B. $a^2+4a+4$
• C. $a^2-2a+1$
• D. $2(a^2+1)$

Answer 1

The correct option is
We know that $(x+y{)}^2=x^2+y^2+2xy$
So, $(a+2{)}^2=a^2+2^2+2\times a\times 2$
$=a^2+4+4a$

We know that $(x-y{)}^2=x^2+y^2-2xy$
So, $(a-1{)}^2=a^2+1^2-2\times a\times 1$
$=a^2+1-2a$

We know that $(x+y)(x-y)=x^2-y^2$
So, $(a+3)(a-3)=a^2-3^2=a^2-9$

Similarly, $(a+1{)}^2+(a-1{)}^2$
$=a^2+1+2a+a^2+1-2a$
$=2a^2+2=2(a^2+1)$