Question

The figures below are rectangles. Which polynomial represents the area of the shaded region? HAVE ALL MY POINTS but answer truthfully cause i have the answer choices

Answer 1

Answer:

$7x - 1$

Step-by-step explanation:

Area of the shaded region = area of the large rectangular - area of the small rectangle

Area of rectangle is given as l*w

Area of the large rectangle = $l*w = (x + 5)(x - 1)$

Expand

$= x(x - 1) +5(x - 1)$

$= x^2 - x + 5x - 5$

Area of large rectangle $= x^2 + 4x - 5$

Area of small rectangle = $l*w = (x + 1)(x - 4)$

$= x(x - 4) +1(x - 4)$

$= x^2 - 4x + x - 4$

Area of small rectangle = $= x^2 - 3x - 4$

Area of shaded region = $(x^2 + 4x - 5) - (x^2 - 3x - 4)$

$= x^2 + 4x - 5 - x^2 + 3x + 4$

Collect like terms

$= x^2 - x^2 + 4x + 3x - 5 + 4$

$= 7x - 1$