**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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