The factored form is 3pq(r + 4q). The value of p³ + q³ - r³ - 3pqr is q³ - 36q + 37.
How to factorize?
1. . Factorizing 3p q r + 12p"q"
The given expression can be factored by grouping:
3p q r + 12p"q" = 3pq(r + 4q)
Therefore, the factored form is 3pq(r + 4q).
2. If p = 4 and 3r+ 6p = 27, find the value of p³ + q³ - r³ - 3pqr
Substituting p = 4 into the equation 3r + 6p = 27:
3r + 6(4) = 27
Solving for r, we find:
3r = 9
r = 3
Now, plug p = 4 and r = 3 into the expression p³ + q³ - r³ - 3pqr:
p³ + q³ - r³ - 3pqr = 4³ + q³ - 3³ - 3(4)(3)(q)
64 + q³ - 27 - 36q = q³ - 36q + 37
Therefore, the value of p³ + q³ - r³ - 3pqr is q³ - 36q + 37.
Complete question:
1. Factorize 3p q r + 12p"q" 1)
2.If p = 4 and 3r+ 6p = 27, find the value of p³ + q³ - r³ - 3pqr