Question

factorise 10(p-2q)^3 + 6(p-2q)^2 - 20(p-2q)​

Answer 1

Answer:

Step by Step Solution

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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)

Step-by-step explanation:

i hope you understand