The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.
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Simplification</h3>
Question 1: a³ - 1000b³
a³ - b³
= (a-b) × (a² +ab +b²)
- 1000 is the cube of 10
- a³ is the cube of a¹
- b³ is the cube of b¹
So,
(a - 10b) × (a² + 10ab + 100b²)
Question 2: 64a³ - 125b³
a³ - b³
= (a-b) × (a² +ab +b²)
- 64 is the cube of 4
- 125 is the cube of 5
- a³ is the cube of a¹
- b³ is the cube of b¹
So,
(4a - 5b) • (16a² + 20ab + 25b²)
Learn more about simplification:
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The choices are in the slope-intecept form: y = mx + b, where m is the slope and b is the y-intercept. Looking at the graph, the y-intercept is the point at which it intersects the y-axis. That would be -1. So, the answer is either the 1st or 2nd choice. Next, we find the slope. Take 2 points that lie along the line. For example, points (1,2) and (2,5). Calculate for the slope.
m = (y2-y1)/(x2-x1)
m = (5-2)/(2-1)
m = 3
Hence, the graph is y = 3x - 1
First you have to convert 1/10 into a decimal:
1/10= 0.1
Multiply 0.1 by 200:
0.1x200=20
So, 20 is 1/10 of 200.
Let x be the number of people that can be seated.
The value of x is some number 0 or greater, such that this number is a whole number (we can't have half a person). This means that

which is the same as saying

The instructions state that we can seat up to 1200 people. This is the max capacity. We can't go over this amount. So we will also have

indicating that x can be less than 1200 or equal to 1200.
So putting the two inequalities together, we get

Note: if you haven't learned about compound inequalities yet, then the teacher may only want

as the answer.