Use the image below to answer the following questions:

Write an expression in expanded form for the area of the shaded region.

Write the expression for the area as a factored polynomial.

Factor the following expression by taking out the common factor:

$8x\left(10y-z+w\right)-9u\left(10y-z+w\right)$8x(10y−z+w)−9u(10y−z+w)

Fully factor $4b\left(4y+5x\right)+c\left(4y+5x\right)+3a\left(4y+5x\right)$4b(4y+5x)+c(4y+5x)+3a(4y+5x).

Factor the following expression:

$4p^2q^2-81c^2d^2$4p2q2−81c2d2

Factor polynomial expressions involving common factors, trinomials, and differences of squares, using a variety of tools and strategies