factorised form of 36p^2+q^2-12pq is
Answers
Answer:
(q-6p)
Step-by-step explanation:
36p^2+q^2-12pq
=(q-2.6p.q+6p)^2
=(q-6p)^2(and)
Proper Question: The factorized form of 36p² + q² - 12pq is?
Answer: The factorized form of the given expression 36p² + q² - 12pq is given as (6p - q)².
Given:
The given expression is 36p² + q² - 12pq.
To Find:
The factorised form of the expression 36p² + q² - 12pq.
Solution:
→ The given expression 36p² + q² - 12pq is a quadratic polynomial of degree 2, therefore it will have 2 factors.
→ We could also write the given expression as 36p² - 12pq + q²
→ To factorise the given expression we would split the middle term:
- The product of the first term and the last term is equal to 36p²q².
- Therefore we would split the middle term of the given expression into two terms such that their product is equal to 36p²q².
- We would split -12pq into -6pq and -6pq.
∵ 36p² - 12pq + q²
∴ 36p² - 6pq - 6pq + q²
∴ 6p(6p - q) - q(6p - q)
∴ (6p - q)(6p - q)
∴ (6p - q)²
→ Therefore on factorisation of (36p² - 12pq + q²) we get (6p - q)².
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