Question

A square corner of 16 square centimeters is removed from a square paper with an area of 9x2 square centimeters. A square. Most of the square is shaded blue. In the bottom right of the square is a smaller square, outlined in a dashed line, and not shaded. Which expression represents the area of the remaining paper shape in square centimeters? (x – 7)(x – 9) (3x – 2)(3x – 8) (3x – 4)(3x + 4) (9x – 1)(x + 16)

Answer 1

Given:

A square corner of 16 square centimeters is removed from a square paper with an area of 9x² square centimeters.

To find:

The area of the remaining paper shape in square centimeters.

Solution:

Initial area of the square paper = 9x² sq. cm

Area of square which is removed from the initial square paper = 16 sq. cm

Subtract area of removed square from the initial area, to find the area of the remaining paper shape.

`9x^2-16=(3x)^2-4^2`

`9x^2-16=(3x-4)(3x+4)`
`[\because a^2-b^2=(a-b)(a+b)]`

Therefore, the area of the remaining paper shape is (3x-4)(3x+4) sq. cm.

Hence, the correct option is C.