EVALUATE NON LINEAR EXPRESSIONS
To evaluate a nonlinear expression, we have to substitute the given values of the variables into the expression and simplify using PEMDAS.
PEMDAS is the rule that can be used to simplify or evaluate complicated numerical expressions with more than one binary operation.
P ----> Parentheses
E ----> Exponent
M ----> Multiply
D ----> Divide
A ----> Add
S ----> Subtract
Important Notes :
1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.
2. Division does not always come before multiplication. We have to do one by one in the order from left to right.
Example 1 :
Evaluate the following expression for x = 3 :
2x2
Solution :
= 2x2
Substitute x = 3.
= 2(3)2
|
= 2(3)2 = 2(9) = 18 |
1Exponent Multiplication Result |
Example 2 :
Evaluate the following expression for x = 2 and y = 3 :
x2 + y2
Solution :
= x2 + y2
Substitute x = 2 and y = 3.
= 22 + 32
|
= 22 + 32 = 4 + 9 = 13 |
1Exponent Addition Result |
Example 3 :
Evaluate the following expression for x = -2 :
3x3
Solution :
= 3x3
Substitute x = -2.
= 3(-2)3
|
= 3(-2)3 = 3(-8) = -24 |
1Exponent Multiplication Result |
Example 4 :
Evaluate the following expression for x = -1 and y = 2 :
x2 + 3y3
Solution :
= x2 + 3y3
Substitute x = -1 and y = 2.
= (-1)2 + 3(2)2
|
= (-1)2 + 3(2)2 = 1 + 3(4) = 1 + 12 = 13 |
1Exponent Multiplication Addition Result |
Example 5 :
Evaluate the following expression for x = 1 and y = -2 :
3x2 - 2y3
Solution :
= 3x2 - 2y3
Substitute x = 1 and y = -2.
= 3(1)2 - 2(-2)3
|
= 3(1)2 - 2(-2)3 = 3(1) - 2(-8) = 3 + 16 = 19 |
1Exponent Multiplication Addition Result |
Example 6 :
Evaluate the following expression for x = 1 and y = 2 :
y2 ÷ 2 + x3
Solution :
= y2 ÷ 2 + x3
Substitute x = 1 and y = 2.
= 22 ÷ 2 + 13
|
= 22 ÷ 2 + 13 = 4 ÷ 2 + 1 = 2 + 1 = 3 |
1Exponent Division Addition Result |
Example 7 :
Evaluate the following expression for x = 3 and y = -1 :
x2 + y + y2
Solution :
= x2 + y + y2
Substitute x = 3 and y = -1.
= 32 + (-1) + (-1)2
|
= 32 + (-1) + (-1)2 = 9 - 1 + 1 = 8 + 1 = 9 |
1Exponent Subtraction Addition Result |
Example 8 :
Evaluate the following expression for x = 6, y = 8 and z = 6.
z2(x + y)
Solution :
= z2(x + y)
Substitute x = 6, y = 8 and z = 6.
= 62(6 + 8)
|
= 62(6 + 8) = 62(14) = 36(14) = 504 |
1Parentheses 1Exponent Multiplication Result |
Example 9 :
Evaluate the following expression for x = 1 and y = 1.
(y3 + x) ÷ 2 + x
Solution :
= (y3 + x) ÷ 2 + x
Substitute x = 1 and y = 1.
= (13 + 1) ÷ 2 + 1
|
= (13 + 1) ÷ 2 + 1 = (13 + 1) ÷ 2 + 1 = (1 + 1) ÷ 2 + 1 = 2 ÷ 2 + 1 = 1 + 1 = 2 |
1Parentheses 1Exponent Parentheses Division Addition Result |
Example 10 :
Evaluate the following expression for y = 3 and z = 7.
z3 - (y ÷ 3 - 1)
Solution :
= z3 - (y ÷ 3 - 1)
Substitute y = 3 and z = 7.
= 73 - (3 ÷ 3 - 1)
|
= 73 - (3 ÷ 3 - 1) = 73 - (3 ÷ 3 - 1) = 73 - (1 - 1) = 73 - 0 = 243 |
1Parentheses 1Division 1Subtraction 1Exponent Result |
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