Question

`(74 xx 74 - 16 xx 16)/(74 + 16)` is equal to ______.

Options

• 90

• 100

• 58

• 68

Answer 1

`(74 xx 74 - 16 xx 16)/(74 + 16)` is equal to 58.

Explanation:

We are asked to simplify:

`(74^2 - 16^2)/(74 + 16)`

Step 1: Recognise the numerator as a difference of squares:

a² – b² = (a – b) (a + b)

Here, a = 74 and b = 16

74² – 16² = (74 – 16) (74 + 16)

Step 2: Substitute into the fraction:

`((74 - 16) (74 + 16))/(74 + 16)`

= 74 – 16 

= 58