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
natima [27]
2 years ago
15

Factorize:(2a - b)² - (a - 2b)²​

Mathematics
2 answers:
bagirrra123 [75]2 years ago
7 0

Answer:

3(a - b)(a + b)

Step-by-step explanation:

Factorize: (2a - b)² - (a - 2b)²​

  • Different of Perfect a Square rule: a²​ - b²​ = (a + b)(a - b)

(2a - b)² - (a - 2b)²​ = [(2a - b) + (a - 2b)] × [(2a - b) - (a - 2b)]

1. Distribute and Simplify:

Distribute the (+) sign on the first bracket and simplify: [(2a - b) + (a - 2b)] → 2a - b + a - 2b → (3a - 3b)

Distribute the (-) sign on the first bracket and simplify: [(2a - b) - (a - 2b)] → 2a - b – a + 2b → (a + b)

We now have:

(3a - 3b)(a + b)

2. Factor out the Greatest Common Factor (3) from 3a - 3b:

(3a - 3b) → 3(a - b)

3. Add "(a + b)" back into your factored expression:

3(a - b)(a + b)

Hope this helps!

faltersainse [42]2 years ago
4 0

Answer:

3[a + b][a - b]

Step-by-step explanation:

Let us recall a useful formula. This formula can factorize any subtraction between perfect squares. The formula is known as a² - b² = (a - b)(a + b).

Let's apply the formula in the given expression as we can see that two perfect squares are being subtracted from each other. Then, we get:

\implies (2a - b)^{2}  - (a - 2b)^{2}

\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]

Since the expression(s) inside the parentheses ( ) cannot be simplified further, we can open the parentheses ( ). Then, we get:

\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]

\implies [2a - b - a + 2b][2a - b + a - 2b]

Now, we can combine like terms and simplify:

\implies [2a - b - a + 2b][2a - b + a - 2b]

\implies [a + b][3a - 3b]

Three is common in 3a - 3b. Thus, we can factor 3 out of the expression:

\implies [a + b][3a - 3b]

\implies [a + b] \times [3a - 3b]

\implies [a + b] \times 3[a - b]

\implies \boxed{3[a + b][a - b]}

Therefore, 3[a + b][a - b] is the factorized expression of (2a - b)² - (a - 2b)²​.

Learn more about factoring expressions: brainly.com/question/1599970

You might be interested in
81 + 7x² +8yt-sx<br> if x = 2 what is the answer
lilavasa [31]

ANSWER:

109 + 8yt - 2s

WORKING:

81 + 7x² + 8yt - sx

81 + 7(2)² + 8yt - s(2)

81 + 7(4) + 8yt - 2s

81 + 28 + 8yt - 2s

81 + 28 + 8yt - 2s

109 + 8yt - 2s

6 0
2 years ago
If you pay $ 34.02 for a jacket that includes a 5% sales tax, what is the price of the jacket before the sales tax?
Jobisdone [24]
105% =$34.02
100% (cost without sales tax) = 34.02/1.05 =$32.40
3 0
3 years ago
Read 2 more answers
Frances can complete 91oil changes in 7 days. How many oil changes can Frances complete in 11days? oil changes
Natali [406]

Answer:

143

Step-by-step explanation:

lets make a fraction:

so

91 oil changes/7days

lets take "x" as the unknown # of oil changes:

so

x/11

91/7=x/11

we can cross multiply:

91*11=7*x

1001=7x

143=x

so 143 oil changes in 11 days

Hope this helps!

4 0
3 years ago
Read 2 more answers
20 units Humulin R insulin in 100 mL of normal saline (NS) to infuse for 20 hours. (Round to the nearest tenth if applicable) a.
wariber [46]

Answer:

a) 1 unit per hour will be infused.

b) 5mL per hour will be infused.

Step-by-step explanation:

Each question can be solved as a rule of three with direct measures, that means we have a cross multiplication.

a. How many units per hour will be infused?

20 units are going to be infused in 20 hours. How many units are going to be infused each hour?

1 hour - x units

20 hours - 20 units

20x = 20

x = \frac{20}{20}

x = 1

1 unit per hour will be infused.

b. How many milliliters per hour will be infused?

100mL are going to be infused in 20 hours. How many mL are going to be infused each hour?

1 hour - x mL

20 hours - 100 mL

20x = 100

x = \frac{100}{20}

x = 5

5mL per hour will be infused.

4 0
3 years ago
Ok this is stressin me out anyone know this
Levart [38]
X=7.
9x-7y=63
9x-7 x 0=63
9x - 0=63
9x=63
X=7.

Y=-9
9 x 0 -7y=63
8 0
2 years ago
Other questions:
  • 15 more than 3 times a number is at most 7
    7·1 answer
  • 3y+4=-8 what does y equal?
    12·2 answers
  • Anyone? Know how to do this?
    13·1 answer
  • What are the discontinuity and zero of the function f(x) = quantity x squared plus 5 x plus 4 end quantity over quantity x plus
    14·1 answer
  • Kegan wants to buy a new skateboard that will cost $140. So far, Kegan has saved $30 toward the purchase to the skateboard. To r
    14·2 answers
  • 96 divided by (7+5) + 19 x 4 =
    7·2 answers
  • we start school at 7:30 a.m. and we get out of school at 2:45 p.m. how long are we at school each day​
    15·1 answer
  • B. Convert years to days.<br> 4 years =<br> .xl<br> year)<br> days)<br> Il<br> days
    14·2 answers
  • Mr. Kelly was checking out his items at Dunkin Donuts, he bought three bags of coffee that cost $6.75 each. There is a sales tax
    6·1 answer
  • Please help:<br> Find the class width of this graph
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!