Answer
15x + 10
Work Step by Step
Larger Rectangle:
A= (x+6)(x+3)
Use FOIL to simplify. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets).
$A= x^{2} + 6x + 3x + 18$ *** Add like terms
$A= x^{2} + 9x + 18 $
Smaller Rectangle:
A= (x-4)(x-2)
Use FOIL to simplify. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets).
$A= x^{2} - 4x - 2x + 8 $ *** Add like terms
$A= x^{2} - 6x + 8 $
Final Area: subtract Area of larger rectangle from Area of smaller rectangle
$A= x^{2} + 9x + 18) - ( x^{2} - 6x + 8 ) $
$A= x^{2} + 9x + 18 - x^{2} + 6x - 8 $
$A= x^{2}- x^{2} + 9x + 6x - 8 + 18 $
$A= 15x + 10 $
