# Chapter 8 - Polynomials and Factoring - Mid-Chapter Quiz - Page 498: 26

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 $A= x^{2} + 9x + 18) - ( x^{2} - 6x + 8 )$ $A= x^{2} + 9x + 18 - x^{2} + 6x - 8$ $A= x^{2}- x^{2} + 9x + 6x - 8 + 18$ $A= 15x + 10$

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