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Question: If z = 10, find the value of \({z^3} - 3\left( {z - 10} \right)\)....

If z = 10, find the value of z3−3(z−10){z^3} - 3\left( {z - 10} \right).

Explanation

Solution

Put the value of z = 10 in z3−3(z−10){z^3} - 3\left( {z - 10} \right) to find the required solution.

Complete step by step solution:
Given z =10
Now z3−3(z−10){z^3} - 3\left( {z - 10} \right)
⇒z3−3z+30\Rightarrow {z^3} - 3z + 30
Putting z = 10
⇒(10)3−3×10+30=1000\Rightarrow {\left( {10} \right)^3} - 3 \times 10 + 30 = 1000
On solving we get
z3−3(z−10)=1000{z^3} - 3\left( {z - 10} \right) = 1000

So, thousand is the correct answer.

Note:
Sometimes this question required factorization to solve them.
Example if expression is x2−7x+10{x^2} - 7x + 10
Then it can be written as
x2−2x−5x+10{x^2} - 2x - 5x + 10
=x(x−2)−5(x−2)= x\left( {x - 2} \right) - 5\left( {x - 2} \right)
=(x−2)(x−5)= \left( {x - 2} \right)\left( {x - 5} \right)
Now we can directly find the answer after putting the value of x in this expression.