Final answer:
To multiply 2(3x - 5) using an area model, we represent 2 times 3x and 2 times -5 on a rectangle, which results in the terms 6x and -10 respectively, giving us the answer 6x - 10.
Step-by-step explanation:
To multiply the expression 2(3x - 5) using an area model, you start by drawing a rectangle and dividing it into two sections, each representing a term in the binomial. One section will represent 2 times 3x, and the other will represent 2 times -5.
Multiplying the first area, we have 2 multiplied by 3x, which equals 6x. The second area is 2 multiplied by -5, which equals -10. So the area model shows that 2(3x - 5) = 6x - 10.
Remember the following rules when multiplying numbers: when two positive numbers multiply, the answer has a +ve sign, e.g., 2x3 = 6. When two negative numbers multiply, the answer also has a +ve sign, e.g., (-4) x (-3) = 12. But when the two numbers multiplied have opposite signs, the answer has a -ve sign, e.g., (-3) x 2 = -6.