Evaluate 745^2 - 38^2.

We factor the denominator as a difference of squares: 745^2 - 38^2 = 7(45 + 38)(45 - 38) = 7(83)(7) = 183.

jmc

algebra junior

Problem

Evaluate

\frac{7}{4 5 ^{2} - 3 8 ^{2}}

Solution

We factor the denominator as a difference of squares:

\frac{7}{4 5 ^{2} - 3 8 ^{2}} = \frac{7}{( 45 + 38 ) ( 45 - 38 )} = \frac{7}{( 83 ) ( 7 )} = \frac{1}{83} .

Final answer

\dfrac{1}{83}