Find P cube minus Q cube if P minus Q is equal to minus 8, PQ is equal

1.	Find P cube minus Q cube if P minus Q is equal to minus 8, PQ is equal to minus 12
Answer» Answer: The value of P³ - Q³ is -224. STEP-by-step EXPLANATION: It is provided that: $P-Q=-8\\PQ=-12$ The formula of (a + b)² and (a - b)² are: $(a+b)^{2}=a^{2}+b^{2}+2ab\\(a-b)^{2}=a^{2}+b^{2}-2ab$ Use these relations to compute the value of P and Q as FOLLOWS: Step 1: Compute the value of P² + Q² as follows: $(P-Q)^{2}=P^{2}+Q^{2}-2PQ\\(-8)^{2}=P^{2}+Q^{2}-(2\times-12)\\64=P^{2}+Q^{2}+24\\P^{2}+Q^{2}=40$ Step 2: Compute the value of P + Q as follows: $(P+Q)^{2}=P^{2}+Q^{2}+2PQ\\=40+(2\times-12)\\=40-24\\=16\\P+Q=4$ Step 3: Add the equations P - Q = -8 and P + Q = 4 as follows; $P + Q = 4\\P - Q = -8\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2P=-4\\P=-2$ Step 4: Use the value of P = - 2 in the equation P + Q = 4 and solve for Q as follows: $P+Q=4\\-2+Q=4\\Q=6$ Step 5: Compute the value of P³ - Q³ as follows: $P^{3} -Q^{3}=(-2)^{3}-(6)^{3}=-8-216=-224$ Hence the value of P³ - Q³ is -224.