All categories

2 years ago

Factorise 1-a^2 b^2

Mathematics

1 answer:

DerKrebs [107]2 years ago

7 0

Hi there.

Thanks for using Brainly!

First, let's rewrite to make this problem easier.

1^2 - a^2b^2

Then we must multiply the terms with equal exponents with their bases.

1^2-(ab)^2

Using the factor: a^2 - b^2=(a-b)(a+b)

We can factor using that expression.

(1-ab) x (1+ab)

After factoring, this has been our solution.

Solution: (1-ab) x (1+ab)

Thanks for using Brainly!

- Tutor John

You might be interested in

Please helpppppppppp

Alika [10]

Answer:

x = 1/3

Step-by-step explanation:

f(x) = -3x^2 + 2x-17

This is in the form

ax^2 +bx+c

a = -3 b = 2 c = -17

The axis of symmetry is at

x = -b/2a

x = -2/ (2*-3)

x = -2/-6

x = 1/3

8 0

3 years ago

Let A be a set of numbers.

LUCKY_DIMON [66]

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

Find $x+y,xy$

$x+y=5m+5n=5(m+n)$

So, $x+y$ is divisible by 5.

$xy=(5m)(5n)=25mn=5(5mn)$

So,

$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

So,

$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

So,

$xy$ ∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

4 0

3 years ago

Consider the given function.

Neporo4naja [7]

The first interception for this function would be at (1,0) the next would be (4,0)

6 0

3 years ago

Read 2 more answers

Write a rational function with no vertical asymptotes and no holes. Please explain.

Ksju [112]

ANSWER

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

EXPLANATION

We write the function such that both the numerator and the denominator are prime.

An example of a rational function with no vertical asymptotes and no holes is

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

For the above rational function, the denominator is never zero, so there are no vertical asymptotes.

Also the highest common factor for the numerator and the denominator is 1 so there are no holes.

4 0

3 years ago

Find the distance between the points (-3,-2) and (1,-5)

Vsevolod [243]

The slope or distance is 4/-3

7 0

3 years ago

Factorise 1-a^2 b^2​

Factorise 1-a^2 b^2