factorise 10(p-2q)³+6(p-2q)²-20(p-2q)
Answers
Step-by-step explanation:
10(p-2q)3+6(p-2q)2-20(p-2q)
Final result :
2 • (p - 2q) • (5p2 - 20pq + 3p + 20q2 - 6q - 10)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((10•((p-2q)3))+(6•((p-2q)2)))-20•(p-2q)
Step 2 :
Equation at the end of step 2 :
((10•((p-2q)3))+6•(p-2q)2)-20•(p-2q)
Step 3 :
Equation at the end of step 3 :
(10•(p-2q)3+6•(p-2q)2)-20•(p-2q)
Step 4 :
Pulling out like terms :
4.1 Pull out p-2q
After pulling out, we are left with :
(p-2q) • ( (p-2q) * (10p-20q+6) +( 20 * (-1) ))
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
10p2 - 40pq + 6p + 40q2 - 12q - 20 =
2 • (5p2 - 20pq + 3p + 20q2 - 6q - 10)
Trying to factor by pulling out :
5.2 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)
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 :
2 • (p - 2q) • (5p2 - 20pq + 3p + 20q2 - 6q - 10)
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Answer:
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