Show that (a + b) (a + b)²=a³+ 3a²b+3ab²+b³

Step-by-step explanation:

(a+b)(a+b)² = (a+b)(a²+2ab+b²)

=a(a²+2ab+b²) + b(a²+2ab+b²)

= a³+2a²b+ab² + a²b+2ab²+b³

=a³+2a²b+ a²b+ab² +2ab²+b³

=a³+3a²b+3ab²+b³

5/109 in the simplest form?

bunch of questios\ns

1. Solve each inequality. Try to solve some using algebra and others using graphing on a number line.
Express each result using interval notation.
(a) x + 5
3
> 2
(b) −2x − 1 ≤ −9
(c) x
2 ≤ 9
2. If a > b > c > d, then which is larger, a + c or b + d? Can we tell from a > b > c > d which of a + d and
b + c is larger? (Problem 9.25 in the textbook, page 283)
If you are stuck, Problems 9.1 and 9.2 in the textbook may help.
3. Back in elementary school, I learned a great magic trick to compare two positive fractions. Here’s
my magic trick in action. Consider the fractions 5
19 and 6
23 . I multiply the numerator of the first and
the denominator of the second, and get 5 · 23 = 115. I multiply the numerator of the second and the
denominator of the first, and get 6 · 19 = 114. Because 115 > 114, I know that 5
19 >
6
23 .
Why does this magic trick work? In other words, if a, b, c, and d are positive, then why does ad > bc
mean that a
b
>
c
d
? (Problem 9.28 in the textbook, page 283)
If you are stuck, Problem 9.3 in the textbook may help.
4. Which number is bigger, −
1227
1229 or −
1229
1231? Do not use a calculator.

Last year, Mr. Smith's biology class averaged 73 on their first test. This year, his new class averaged 87 on the
same test. Based on these results, is it reasonable to conclude that this year's class is more intelligent?
O Yes, a grade of 87 is higher than a grade of 73.
O Yes, the study was done in an academic setting.
O No, the experiment was not double-blind.
No, there was no use of a placebo in the experiment.
O No, there may be other differences between the two years besides the grades.

Can you please help
Plzzzzzz

When a number is decreased by 4%, the result is 66. What is the original number to the nearest tenth?

Twenty percent of the shoes in a factory are black. One shoe is chosen and replaced. A second shoe is chosen and replaced. Then a third shoe is chosen. What is the probability that none of the shoes are black? The probability that none of the shoes are black is .

A business building has several office spaces for rent. Each
office is in the shape of a right triangle. If one side of the
office is 11 feet long and the longest side is 15 feet long,
what is the length of the other side?

What is the equation in slope-intercept form of a line that passes through the point (4, 5) and has a slope of 12?
Y=_x+_

The area of a square backyard is
400 square meters. What is the
length of each side of the
backyard?

Devide : 72x2y2z by - 12 xyz​

Someone please help me(Ik it’s not B)

71.9 divide by 8 using long division.

The sum of three numbers is 41.
The second number is 5 times the first.
The third number is 14 less than the second.
What is the third number?

On Monday, I bought 23 strawberries. On Tuesday, I ate 8 of the strawberries. Now, I want to divide the remaining strawberries into bags of 5 strawberries each.

6.12 x 10^4 ? 612,000

Find the missing term: 1, 1.5, x, 2.5, 3,

Mary says that -5 x 2 = -3. Explain the mistake Mary made and write the correct number sentence including the correct answer.

Help me please I need an answer asap
Which of the following statements would best represent the value of a? PLEASE HELP

Multiply.

(−2/3)(5/4)

Enter your answer as a fraction thats in simplest form.

If tax was 8.25% on the $220 total for the items purchased at Target, what was the total cost of the items including tax?

(8x*+ 6x -6 ) + (3x- 7 +5)

For the lunch special at a high school cafeteria, students can get either salad or french fries as a side order. The following table shows the number of each side order for the lunch specials purchased on one day, classified by the grade of the student
Grade 9
Grade 10
Grade 11
Grade 12
Total
Salad
37
34
21
28
120
83
71
57
37
248
French fries
Total
120
105
78
65
368

From those who purchased the lunch special that day, one student will be selected at random. What is the probability that the student selected will be in grade 10 given that the student ordered
french fries as the side order?
A
71/368
B
105/368
C
71/245
D
245/308

Proportional means
Check ALL that apply.
*
same
equal
different
other

Thanks for the Help, i love you guys

How do you calculate rate of change?

Kayla's backyard is a rectangle with dimensions of 18 feet by 22 feet. If she covers the ground with a circular hot tub with a diameter of 14 feet, what is the approximate area of the ground, in square feet, that remains exposed?

jim drives 350 miles in 5 hours hopw long does he drive in 1 hour

Which represents a side length of a square that has an area of 288 square inches?

Evaluate each using the values given.

1. 6c(a+a+a); use a=1, and c=3

NEED HELP ASAP PLEASE HELPPPP!!!

The area of a rectangular warehouse measures 4,288 square feet. The width of the warehouse is 64 feet long. Draw a model to represent the problem, and then solve for the length of the warehouse. Use paper to show your work.