1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DaniilM [7]
3 years ago
15

6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a² + b² + ab) – (a + b) (a² + b²– ab) iii) (b² – 49) (b + 7) + 3

43
Mathematics
1 answer:
Shkiper50 [21]3 years ago
6 0

Step-by-step explanation:

<h2>i).</h2>

(a + b)(5a – 3b) + (a – 3b)(a – b)

Expand each of the terms separately

That's

(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²

= 5a² + 2ab - 3b²

(a – 3b)(a – b) = a² - ab - 3ab + 3b²

= a² - 4ab + 3b²

<u>Add the terms</u>

That's

5a² + 2ab - 3b² + a² - 4ab + 3b²

<u>Group like terms</u>

5a² + a² + 2ab - 4ab - 3b² + 3b²

We have the answer as

<h2>6a² - 2ab</h2>

<h2>ii)</h2>

(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)

Expand the terms separately

<u>For (a – b) (a² + b² + ab)</u>

Using the rule

x³ - y³ = (x - y)( x² + xy + y²) expand the expression

So we have

(a – b) (a² + b² + ab) = a³ - b³

<u>For (a + b) (a² + b²– ab)</u>

Using the rule

x³ + y³ = (x + y)( x² - xy + y²) expand the expression

We have

(a + b) (a² + b²– ab) = a³ + b³

Subtract the terms

That's

a³ - b³ - (a³ + b³)

Remove the parenthesis

a³ - b³ - a³ - b³

Group like terms

a³ - a³ - b³ - b³

We have the final answer as

<h2>-2b³</h2>

<h2>iii)</h2>

(b² – 49) (b + 7) + 343

Expand the terms

That's

b³ + 7b² - 49b - 343 + 343

We have the final answer as

<h2>b³ + 7b² - 49b</h2>

Hope this helps you

You might be interested in
Given the following sequence, find the 25th term: 0, 1, 2, 3, 4, . . .
Burka [1]
The answer for this question would be 24 because 0 is included.
8 0
3 years ago
Each drink cost d in dollars
zhenek [66]
There is no picture what do you mean
6 0
2 years ago
The Columbia Tower in Seattle is 954 feet tall. The Seafirst Tower is T feet tall and d feet away from the Colombia Tower. Find
Blababa [14]
You have to include a drawing that relates the distace between de towers and some angles.

I will use one that gives the angle from the base of Seafirst Tower to the top of Columbia tower as 53 degress.

This lets you calculate the distance between the towers, d, as

tan(53) = 954 / d => d = 954 / tan(53) = 718.89ft

The same drawing gives the angle from the the base of the Columbtia tower to the top of the Seafirst Tower as 27 degrees.

Tnen, tan(27) = height / d => height = d*tan(27) = 718.89*tan(27) = 366.29 ft

Answer: 366.29 ft


6 0
3 years ago
Please help me solve this before 8pm today please!!!!!
Nastasia [14]

Answer: x=10

Step-by-step explanation:

7776^{x+5}=216^{3x-5}

6^{5(x+5)}=6^{3(3x-5)}

5(x+5)=3(3x-5)

5x+25=9x-15

25=4x-15

4x=40

x=10

8 0
1 year ago
Can somebody please help me with (d)?
lapo4ka [179]
I’m in middle school so if u show me I’ll be able to help I’m one of those people
4 0
3 years ago
Other questions:
  • A garden measures 6 feet by 7 feet. A gravel path of constant width is placed around the garden so that the total area is 72 squ
    9·2 answers
  • Write the equation of the line that passes through (3,-2) and has a slope of 4 in point-slope form
    14·1 answer
  • PLEASE PLEASE PLEASE HELP AND QUICK
    10·1 answer
  • Answer as a fraction in lowest terms:
    7·1 answer
  • Trigonometry problems, help
    11·1 answer
  • Hunter jogs 6 miles in 30 minutes. What is his rate?<br> What is his rate?
    15·1 answer
  • 6) Find the value of y. (pic below)
    5·2 answers
  • 8+4=<br> write the answer below
    13·1 answer
  • Write the numbers three hundred and fifty-four thousand, two hundred and ten in figures (354,210).
    9·1 answer
  • Can someone fill this out thanks
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!