To determine the value of the expression [tex]\( 4 \sqrt{a^2 - b^2} \)[/tex] when [tex]\( a = -5 \)[/tex] and [tex]\( b = 3 \)[/tex], follow these steps:
1. Compute [tex]\( a^2 \)[/tex]:
[tex]\[
a = -5 \implies a^2 = (-5)^2 = 25
\][/tex]
2. Compute [tex]\( b^2 \)[/tex]:
[tex]\[
b = 3 \implies b^2 = 3^2 = 9
\][/tex]
3. Subtract [tex]\( b^2 \)[/tex] from [tex]\( a^2 \)[/tex]:
[tex]\[
a^2 - b^2 = 25 - 9 = 16
\][/tex]
4. Take the square root of the result:
[tex]\[
\sqrt{16} = 4
\][/tex]
5. Multiply by 4:
[tex]\[
4 \times 4 = 16
\][/tex]
Therefore, the value of the expression [tex]\( 4 \sqrt{a^2 - b^2} \)[/tex] when [tex]\( a = -5 \)[/tex] and [tex]\( b = 3 \)[/tex] is [tex]\( \boxed{16} \)[/tex].
