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Find the HCF: $m^3-m^2-m+1, 2m^4-2m and 3m^2+3m-6$.

This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the description below. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts.

Solution:
Given,

$1^{st} expression = m^4-m^2-m+1$

= $m^2(m^2-1) -1(m-1)$

= $(m^2-1)(m-1)$

= $(m+1)(m-1)(m-1)$

$2^{nd} expression = 2m^4-2m$

= $2m(m^3-1)$

= $2m(m-1)(m^2+m+1)$


$3^{rd} expression = 3m^2+3m-6$

= $3m^2+(6-3)m-6$

= $3m^2+6m-3m-6$

= $3m(m+2) -3(m+2)$

= $(3m-3)(m+2)$

= $3(m-1)(m+2)$


Therefore, the HCF = $(m-1)$

Explanation to the above answer.


Step 1: Write the first expression given in the question.

Step 2: Take the common of the first two and last two terms. 

Step 3:  Write the expression in factor form.

Step 4: The fist factor in the expression is in the form of (a²-b²). So, write it as (a+b)(a-b).

Step 5: Write the second expression given in the question.

Step 6: Take the common factor and re-write the expression.

Step 7: As we had (a³-b³) in above step, we write it in factor form as (a-b)(a²+ab+b²).

Step 8: Write the third expression given in the question.

Step 9: Using mid-term factorization method, write 3m as (6-3)m.

Step 10: Re-write the expression after opening the parenthesis.

Step 11: Take common between the first two and last two terms of the expression.

Step 12: Write the expression in factor form.

Step 13: We get 3 common in one of the factor so, rewrite it by taking 3 as a common factor.

Step 14: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (m-1) are the common factors.

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Question: Find the HCF: m³-m²-m+1, 2m³-2m, 3m²+3m-6. | HCF and LCM | SciPiPupil

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