Question

5 times 19 = 95but i have to use the formula:(a + b) (a - b) = a^2 - b^2

Answer 1

The first thing to do to is to get the values of 'a' and 'b'

The only wat to get that is to resolve the expression simultaneously.

5 x 19 = ( a + b ) x ( a - b ),

so a + b = 5 ---- ( equation 1 ),

a - b = 19 ---- ( equation 2 )

solving simultaneously,

$\begin{gathered} \text{frpm equation 1, b = 5 - a }---\text{ ( equation 3 )} \\ \text{Substitute it into equation 2 } \\ a\text{ - ( 5 - a ) = 19 } \\ a\text{ - 5 + a = 19 } \\ 2a\text{ = 19 + 5 } \\ 2a\text{ = 24 } \\ a\text{ = }\frac{24}{2} \\ a\text{ = 12 } \\ (\text{ substitute a = 12 into equation 3 ) } \\ b=\text{ 5 - a } \\ b\text{ = 5 - 12 } \\ b\text{ = -7} \end{gathered}$

Hence, since a = 12 and b = -7

$a^2-b^2=12^2-(-7)^2\text{ = 144 - 49 = 95 }$