EVALUATE NON LINEAR EXPRESSIONS
About "Evaluate nonlinear expressions"
Evaluate nonlinear expressions :
Here we are going to learn, how to evaluate non linear expressions.
A linear expression is an algebraic expression in which each term is either a constant or the product of a constant and (the first power of) a single variable (however, different variables may occur in different terms). ...
Expressions with exponents greater than one are non-linear.
Example 1 :
Evaluate the following using the given values.
y² ÷ 2 + x³, use x = 1 and y = 2
Solution :
Now we have to apply the values of x and y in the given expression.
= y² ÷ 2 + x³
= 2² ÷ 2 + 1³
= 4 ÷ 2 + 1
According to order of operation, first we have to perform division and then addition.
= 2 + 1 = 3
Hence the answer is 3.
Example 2 :
Evaluate the following using the given values.
x² + y + y²; use x = 3, and y = -1
Solution :
= x² + y + y²
= 3² + (-1) + (-1)²
= 9 -1 + 1
= 9
Hence the value of the given expression is 9.
Example 3 :
Evaluate the following using the given values.
z²(x + y); use x = 6, y = 8, and z = 6
Solution :
= z²(x + y)
= 6²(6 + 8)
= 36(14)
= 504
Hence the value of the given expression is 504.
Example 4 :
Evaluate the following using the given values.
(y³ + x) ÷ 2 + x; use x = 1, and y = 1
Solution :
= (y³ + x) ÷ 2 + x
= (1³ + 1) ÷ 2 + 1
Simplify the numbers which are inside the bracket first
= 2 ÷ 2 + 1
Now we have to divide
= 1 + 1
= 2
Hence the value of the given expression is 2.
Example 5 :
Evaluate the following using the given values.
z³ − (y ÷ 3 − 1); use y = 3, and z = 7
Solution :
= z³ − (y ÷ 3 − 1)
= 7³ − (3 ÷ 3 − 1)
Simplify the numbers which are inside the bracket first
= 243 − (1 − 1)
= 243 − 0 ==> 243
Hence the value of the given expression is 243.
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