# EVALUATE NON LINEAR EXPRESSIONS

Evaluate nonlinear expressions :

Here we are going to learn, how to evaluate non linear expressions.

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

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.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate nonlinear expressions".

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