Factorise 36a^2b^2 - 2ab^2c +48 abc^4
Answers
Correct Question -
- Factorise :- 36a²b² - 2ab²c + 48abc⁴.
Answer -
- 2ab (24c⁴ + 18ab + bc).
What to do?
- Factorise 36a²b² - 2ab²c + 48abc⁴.
Step-by-step explanation -
- Here we are asked to factorise 36a²b² - 2ab²c + 48abc⁴. We will do so by taking out the common factors!
We are going to use the following procedure for factorising the given polynomial :-
1. Find the HCF of all the terms of the given polynomial.
2. Divide each term of the given polynomial by the HCF. Enclose the quotient within the brackets and keep the common factor outside the bracket.
→ 36a²b² - 2ab²c + 48abc⁴
Here,
- HCF of 36a²b², 2ab²c and 48abc⁴ = 2ab.
Therefore,
→ 36a²b² - 2ab²c + 48abc⁴
→ 2ab (24c⁴ + 18ab + bc)
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Verification -
- To check our answer, let's multiply 2ab with 24c⁴ + 18ab + bc and see whether we get 36a²b² - 2ab²c + 48abc⁴.
→ 2ab (24c⁴ + 18ab + bc)
→ 2ab (24c⁴) + 2ab (18ab) + 2ab (bc)
→ 48abc⁴ + 2ab (18ab) + 2ab (bc)
→ 48abc⁴ + 36a²b² + 2ab (bc)
→ 48abc⁴ + 36a²b² + 2ab²c
We get 36a²b² - 2ab²c + 48abc⁴ on multiplying 2ab with 24c⁴ + 18ab + bc
Hence verified!!
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