Question

Fully factorise ab+abc+abcd+abd
Hence, or otherwise, work out the values of a, b, c and d using the following additional facts.
ab+abc+abcd+abd=420
a, b, c and d are distinct primes
a>b>c>d

Answer 1

Answer:

How many different prime numbers are factors of the positive integer n?

(1) 4 different prime numbers are factors of 2n --> if itself has 2 as a factor (eg ) than its total # of primes is 4 but if doesn't have 2 as a factor (eg ) than its total # of primes is 3. Not sufficient.

(2) 4 different prime numbers are factors of n^2 --> (where is an integer ) will have as many different prime factors as integer , exponentiation doesn't "produce" primes. So, 4 different prime numbers are factors of . Sufficient.

Answer 2

Step-by-step explanation:

ab+abc+abcd+abd

ab(1+c)+abd(c+1)

(ab+abd)(c+1)

ab(1+d)(1+c)

Now Given Also

ab(1+d)(1+c)=420

Find the Factors of 420

=21×2×10

=3×7×2×2×5

=2²×3×7×5

See We Got Four Distinct Number But 2²=4 is Not prime so

ab(1+d)(1+c)=420

Take 1+d=2²

d=3 that is Prime

1+c=3

c=2. that is Prime

a=5

b=7

So

a=5

b=7

c=2

d=3

Order of Values May differ But That Doesn't matter .Like In given a>b>c>d but u can Change order Of my Values like

a=7,b=5,c=3,d=2 this will not matter

Thanks

Mark Brainliest if u liked it