Question

Find the value of $3P\left( {{P^2} + {Q^2}} \right)$ at $P = 0$ , $Q = 1$
A. $0$
B. $1$
C. $3$
D. $5$

Answer 1

Hint : First, we shall analyze the given information so that we are able to solve the given problem. Here we are given an expression $3P\left( {{P^2} + {Q^2}} \right)$
We are asked to calculate the value of $3P\left( {{P^2} + {Q^2}} \right)$ at $P = 0$ , $Q = 1$
For this question, we shall first expand the given expression. Then, we need to substitute the given values $P$ and $Q$ to obtain the required answer.

Complete step-by-step solution:
The given expression is $3P\left( {{P^2} + {Q^2}} \right)$
We need to expand the given expression.
That is, we need to multiply the term $3P$ with the terms that are inside the brackets.
Thus, we get
$3P\left( {{P^2} + {Q^2}} \right) = 3{P^3} + 3P{Q^2}$
 Now, we shall substitute the given values $P = 0$ , $Q = 1$ on the above expression.
That is $3P\left( {{P^2} + {Q^2}} \right) = 3{\left( 0 \right)^3} + 3 \times 0 \times {1^2}$
                                      $ = 0$
Hence, we got $3P\left( {{P^2} + {Q^2}} \right) = 0$ which is the required answer.

Additional information:
Simplification of an expression is the process of changing the expression effectively without changing the meaning of an expression.
 In some questions, we need to apply the BODMAS rule (i.e.) we need to calculate the brackets first and then orders, then division or multiplication, and finally we need to add or subtract.
Moreover, various steps are involved to simplify an expression. Some of the steps are listed below:
If the given expression contains like terms, we need to combine them.
Example: $3x + 2x + 4 = 5x + 4$
We need to split an expression into factors (i.e) the process of finding the factors for the given expression.
Example: ${x^2} + 4x + 3 = (x + 3)(x + 1)$
We need to expand an algebraic expression (i.e) we have to remove the respective brackets of an expression.
Example: $3(a + b) = 3a + 3b$.
We need to cancel out the common terms in an expression.

Note: Here we are given an expression $3P\left( {{P^2} + {Q^2}} \right)$. Here in this question, to find the value of the given expression, we can also substitute the given values on the expression directly. Here, we solved it by expanding the given expression. But, we can also solve without expanding the expression. Hence, we can get the same answer $3P\left( {{P^2} + {Q^2}} \right) = 0$