. Factorize a² +3ab - 5ab - 15b²

Mathematics

1 answer:

kipiarov [429]4 years ago

4 0

Answer:

a² +3ab - 5ab - 15b² = (a+3b) (a-5b)

Step-by-step explanation:

We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,

$a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)$

Now taking a common from the first two terms and 3b from last two terms, then :

$(a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)$

In the above expression, a factor (a-5b) is in both the terms. It would mean that,

$a(a-5b)+3b(a-5b)=(a+3b)(a-5b)$

So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).

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4 years ago

Read 2 more answers

Find the number of distinct permutations of the word "CALCULATOR."

11111nata11111 [884]

Given:

The word is "CALCULATOR."

To find:

The number of distinct permutations.

Solution:

In the word "CALCULATOR",

The number of letters = 10

In which, we have 2 C, A, L and 1 U, T, O, R.

We know that,

$^nC_r=\dfrac{n!}{(n-r)!}$

$^nC_n=\dfrac{n!}{(n-n)!}=n!$

To find the number of distinct permutations of the given word need to divide permutation of all letter by the permutations of repeated letters.

$\text{Total ways}=\dfrac{^{10}C_{10}}{^2C_2\ ^2C_2\ ^2C_2\ ^1C_1\ ^1C_1\ ^1C_1\ ^1C_1}$

$\text{Total ways}=\dfrac{10!}{2!2!2!1!1!1!1!}$

$\text{Total ways}=\dfrac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 2\times 2\times 1\times 1\times 1\times 1}$