Question

Factorize 10(p-2q)3+6(p-2q)2-20(p-2q)

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

2 • (p - 2q) • (5p2 - 20pq + 3p + 20q2 - 6q - 10)

Given:

10(p-2q)3+6(p-2q)2-20(p-2q)

To find:

Factorise the equation

Solution:

10(p-2q)3+6(p-2q)2-20(p-2q)

Taking out 2(p-2q) common from all the terms

After pulling out, we are left with :

(p-2q) • ( (p-2q)  *  (10p-20q+6) +( 20  *  (-1) ))

Pulling out like terms :

1.   Pull out like factors :

10p2 - 40pq + 6p + 40q2 - 12q - 20  =

2 • (5p2 - 20pq + 3p + 20q2 - 6q - 10)

Trying to factor by pulling out :

2 . Factoring:  5p2 - 20pq + 3p + 20q2 - 6q - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  5p2 + 3p

Group 2:  -20pq + 20q2

Group 3:  -6q - 10

Pull out from each group separately :

Group 1:   (5p + 3) • (p)

Group 2:   (p - q) • (-20q)

Group 3:   (3q + 5) • (-2)

Looking for common sub-expressions :

Group 1:   (5p + 3) • (p)

Group 3:   (3q + 5) • (-2)

Group 2:   (p - q) • (-20q)

Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Final result :

2 • (p - 2q) • (5p2 - 20pq + 3p + 20q2 - 6q - 10)

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