Simplify the expression and find its values if $a=-1, b=-3$.$4 a^{2}-b^{2}+6 a^{2}-7 b^{2}$

Given :

The given expression is $4 a^{2}-b^{2}+6 a^{2}-7 b^{2}$;  $a=-1, b=-3$.

To do :

We have to simplify the expression and find its value.

Solution :

$4 a^{2}-b^{2}+6 a^{2}-7 b^{2}$.

$4 a^{2}-b^{2}+6 a^{2}-7 b^{2} = 4 a^{2}+6 a^{2}-7 b^{2}-b^{2}$

$ = 10 a^2 - 8 b^2$

Substitute $a=-1, b=-3$ in the given expression.

$10 a^2 - 8 b^2$

$ = 10 (-1)^2 - 8 (-3)^2$

$= 10 (1) - 8 (9)$

$ = 10 - 72 = -62$.

Therefore, the value of given expression is $-62$.