Given:
The statement is
[tex](4p^2-3q)^2+48p^2q=(4p^2+3q^2)[/tex]
To prove:
The given statement.
Solution:
We have,
[tex](4p^2-3q)^2+48p^2q=(4p^2+3q^2)[/tex]
Now,
[tex]LHS=(4p^2-3q)^2+48p^2q[/tex]
Using [tex](a-b)^2=a^2+b^2-2ab[/tex], we get
[tex]LHS=(4p^2)^2+(3q)^2-2(4p^2)(3q)+48p^2q[/tex]
[tex]LHS=(4p^2)^2+(3q)^2-24p^2q+48p^2q[/tex]
[tex]LHS=(4p^2)^2+(3q)^2+24p^2q[/tex]
It can be rewritten as
[tex]LHS=(4p^2)^2+(3q)^2+2(4p^2)(3q)[/tex]
Using [tex](a+b)^2=a^2+b^2+2ab[/tex], we get
[tex]LHS=(4p^2+3q^2)[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
