The length of a postcard is (3p + 4) centimeters. The width is (p - 2) centimeters. Write the algebraic expression that represents the area of the postcard and simplify.
(3p+4)(p-2)
= 3p (p-2) + 4 (p-2)
= 3 p^2 - 6 p + 4 p - 8
= 3 p^2 - 2 p - 8
To find the area of the postcard, we need to multiply the length by the width. The length is given as (3p + 4) centimeters and the width is given as (p - 2) centimeters.
So, the algebraic expression representing the area of the postcard is:
Area = (3p + 4)(p - 2)
To simplify this expression, we need to multiply the terms using the distributive property:
Area = (3p)(p) + (3p)(-2) + (4)(p) + (4)(-2)
= 3p^2 - 6p + 4p - 8
= 3p^2 - 2p - 8
Therefore, the simplified algebraic expression representing the area of the postcard is 3p^2 - 2p - 8.