a.$−4y(5x+8y)$

• Step 1(a):

  Make and label a generic rectangle.

  $-4y$
  	$5x$	$+8y$

  Step 2(a):

  Fill in the boxes, and then add the boxes' labels together

  $-4y$	$-20xy$	$-32y^2$
  	$5x$	$+8y$

  Answer (a):

  $−20xy−32y^2$

2. $9x(−4+10y)$

• Step 1(b):

  Distribute the $9x$ over each of the terms in the parentheses.

  $9x(−4)+9x(10y)$

  Step 2(b):

  Simplify.

  Answer (b):

  $−36x+90xy=90xy−36x$

3. $(x^2−2)(x^2+3x+5)$

• Hint (c):

  Try using a generic rectangle to solve this problem.

  Answer (c):

  $x^4+3x^3+3x^2−6x−10$