Question

Simplify the given expression.
4(-3p^3q^3 + 2p^2q^2- pq^2 + 4) – 14(-p^3q^3– 2p^2q^2– pq^2 +1)

please fast ​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

 (4•((((0-((3•(p3))•(q3)))+((2•(p2))•(q2)))-(p•(q2)))+4))-(14•((((0-((p3)•(q3)))-(2p2•q2))-pq2)+1))

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  -p3q3 - 2p2q2 - pq2 + 1  =  

 -1 • (p3q3 + 2p2q2 + pq2 - 1)  

Checking for a perfect cube :

3.2    p3q3 + 2p2q2 + pq2 - 1  is not a perfect cube

Equation at the end of step

3

:

 (4•((((0-((3•(p3))•(q3)))+((2•(p2))•(q2)))-(p•(q2)))+4))--14•(p3q3+2p2q2+pq2-1)

STEP  

4

:

Equation at the end of step

4

:

 (4•((((0-((3•(p3))•(q3)))+(2p2•q2))-pq2)+4))--14•(p3q3+2p2q2+pq2-1)

STEP  

5

:

Equation at the end of step

5

:

 (4•((((0-(3p3•q3))+2p2q2)-pq2)+4))--14•(p3q3+2p2q2+pq2-1)

STEP

6

:

Checking for a perfect cube

6.1    -3p3q3+2p2q2-pq2+4  is not a perfect cube

Equation at the end of step

6

:

 4•(-3p3q3+2p2q2-pq2+4)--14•(p3q3+2p2q2+pq2-1)

STEP

7

:

STEP

8

:

Pulling out like terms

8.1     Pull out like factors :

  2p3q3 + 36p2q2 + 10pq2 + 2  =  

 2 • (p3q3 + 18p2q2 + 5pq2 + 1)  

Checking for a perfect cube :

8.2    p3q3 + 18p2q2 + 5pq2 + 1  is not a perfect cube

Final result :

 2 • (p3q3 + 18p2q2 + 5pq2 + 1)