Question

Factorise- 8(p-2q)²-2q+4q-1

Answer 1

8p2 - 32pq - 2p + 32q2 + 4q - 1

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((8 • (p - 2q)2 - 2p) + 4q) - 1

Step 2 :

Trying to factor by pulling out :

2.1 Factoring: 8p2-32pq-2p+32q2+4q-1

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

Group 1: 8p2-2p

Group 2: -32pq+32q2

Group 3: 4q-1

Pull out from each group separately :

Group 1: (4p-1) • (2p)

Group 2: (p-q) • (-32q)

Group 3: (4q-1) • (1)

Looking for common sub-expressions :

Group 1: (4p-1) • (2p)

Group 3: (4q-1) • (1)

Group 2: (p-q) • (-32q)

Bad news !! Factoring by pulling out fails :

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

Final result :

8p2 - 32pq - 2p + 32q2 + 4q - 1

Answer 2

Final result :

 8p2 - 32pq - 2p + 32q2 + 4q - 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((8 • (p - 2q)2 -  2p) +  4q) -  1

Step  2  :

Trying to factor by pulling out :

2.1      Factoring:  8p2-32pq-2p+32q2+4q-1  

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

Group 1:  8p2-2p  

Group 2:  -32pq+32q2  

Group 3:  4q-1  

Pull out from each group separately :

Group 1:   (4p-1) • (2p)

Group 2:   (p-q) • (-32q)

Group 3:   (4q-1) • (1)

Looking for common sub-expressions :

Group 1:   (4p-1) • (2p)

Group 3:   (4q-1) • (1)

Group 2:   (p-q) • (-32q)

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