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
Georgia [21]
3 years ago
15

Use the difference of two squares identity to factor each of the following expressions. (a) x²-81 (b) (3x+y)² -(2y)² (c) 4-(x-1)

² (d) (x+2)²-(y-2)²
Mathematics
1 answer:
ioda3 years ago
4 0

Answer:

a) x^2-9^2=(x+9)(x-9)

b) (3x+y)^2-(2y)^2=(3x+3y)(3x-y)

c) 2^2-(x-1)^2=(1+x)(3-x)

d) (x+2)^2-(y-2)^2=(x+y)(x-y+4)

Explanation:

Factor the expression using difference of two squares.

Formula:

a^2-b^2=(a+b)(a-b)

Part a)  x²-81

write 81 as perfect square.

x^2-9^2

a\rightarrow x

b\rightarrow 9

x^2-9^2=(x+9)(x-9)

Part b) (3x+y)² -(2y)²

a\rightarrow 3x+y

b\rightarrow 2y

(3x+y)^2-(2y)^2=(3x+y+2y)(3x+y-2y)

(3x+y)^2-(2y)^2=(3x+3y)(3x-y)

Part c) 4-(x-1)²

write 4 as perfect square,

2^2-(x-1)^2

a\rightarrow 2

b\rightarrow x-1

2^2-(x-1)^2=(2+x-1)(2-x+1)

2^2-(x-1)^2=(1+x)(3-x)

Part d) (x+2)²-(y-2)²

a\rightarrow x+2

b\rightarrow y-2

(x+2)^2-(y-2)^2=(x+2+y-2)(x+2-y+2)

(x+2)^2-(y-2)^2=(x+y)(x-y+4)

You might be interested in
A supermarket has found that 60% of their customers spend more than $75 each visit. Whats the probability that the next 2 custom
spin [16.1K]
Answer: 0.36 or 36%
60%=60/100=0.6

60% is the same as saying 60/100 or 0.6

To solve for the probability of this problem, we have to, multiply the odds of the two separate events together

event1 is a customer that spends more than 75$. The odds of that happening are .6

event 2 is a customer that spends more than 75$. The odds of that happening are .6

probability=event1*event2
probability=.6*.6 
probability=.36 or 36%
7 0
3 years ago
What are the factors of 24, 30, 42
motikmotik
Factors of 24: 1,2,3,4,6,8,12,24
factors of 30: 1,2,3,5,6,10,15,30
factors of 42: 1,2,3,6,14,21,42
3 0
3 years ago
It cost you $12 to start up your
brilliants [131]

Step-by-step explanation:

let no. of hours be x.

45x - 12 ≥ 117

45x ≥ 129

x ≥ 2.8667 (5sf)

therefore, 3 hours (round up to next whole number).

Topic: inequalities

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

6 0
3 years ago
Choose an appropriate metric unit of a typical house cat
valentina_108 [34]
Your answer is gram hope this helps that is what unit to use  :)
8 0
3 years ago
One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the
Kipish [7]

Let's call the two numbers s and l.


Given these variables, we can say: s = l - 14, based on the first sentence in the problem.


Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}


To solve, we can simply substitute l -14 in for s in the second equation and solve.

\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}

  • Set up

\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}

  • Get terms on the left side to a common denominator for easier addition

\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}

  • Simplify

4(6l - 70) = l(l - 14)

  • Cross multiplication (\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc)

24l - 280 = l^2 - 14l

  • Simplify

l^2 - 38l + 280 = 0

  • Subtract 24l - 280 from both sides of the equation

(l - 10)(l - 28) = 0

  • Factor left side of the equation

l = 10, 28

  • Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

s = 10 - 14 = -4,

Since s is not positive in this case, l = 10 is not a solution.


Thus, l = 28 is our only solution. In this case,

s = 28 - 14 = 14,

which means that the smaller number is 14 and the larger number is 28.

5 0
3 years ago
Other questions:
  • will mark brainles if answered fast There are 72 items on Ginny bookshelf 1/3 of items are hardcover books. 4/9 of the items are
    7·1 answer
  • 4x-y+2z=-6,-2x+3y-z=8,2y+3z=-5
    14·1 answer
  • Which equations below represent a proportional relationship? Select all that apply.
    15·1 answer
  • Write the number in scientific notation.
    14·1 answer
  • -5 (-1 + 6)need help ​
    7·1 answer
  • What is the answer to question
    14·1 answer
  • The initial number of views for a reader board was 25. The number of views is growing exponentially at a rate of 18% per week.
    12·1 answer
  • What is the area of this isosceles trapezoid?
    14·1 answer
  • allenbrights electronics is having a 25% off sale. If the ratio is sale priced at $135 what is the regular price?
    10·1 answer
  • The dog park had 14 dogs in it .6 of the dogs we're huskies .8 of the dogs were mutts . Write the ratio of huskies to mutts as t
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!