You’ll be able to consider algebraic expressions while you substitute numbers for the variables within the algebraic expressions after which comply with the order of operations.

## Extra examples displaying how one can consider algebraic expressions with out exponents

Instance #1

Consider 2a + b + 1 for a = 3 and b = 5

Substitute 3 for a and 5 for b

2a + b + 1 = 2 × 3 + 5 + 1

First, multiply 2 and 3

2a + b + 1 = 6 + 5 + 1

Add from left to proper beginning with 6 and 5

2a + b + 1 = 11 + 1

Lastly, add 11 and 1

2a + b + 1 = 12

Instance #2

Consider a + 4b – ab for a = 2 and b = -1

Substitute 2 for a and -1 for b

a + 4b – ab = 2 + 4(-1) – (2)(-1)

First, multiply 4 and -1 and in addition 2 and -1

a + 4b – ab = 2 + -4 – (-2)

Add the alternative when subtracting

a + 4b – ab = 2 + -4 + 2

Add from left to proper beginning with 2 and -4

a + 4b – ab = -2 + 2

Lastly, add -2 and a couple of

a + 4b – ab = 0

Instance #3

Consider a + 4a ÷ b – 3b for a = 5 and b = -4

Substitute 5 for a and -4 for b

a + 4a ÷ b – 3b = 5 + 4(5) ÷ -4 – 3(-4)

First, multiply 4 and 5

a + 4a ÷ b – 3b = 5 + 20 ÷ -4 – 12

Divide 20 by -4

a + 4a ÷ b – 3b = 5 + -5 – 12

Add the alternative when subtracting

a + 4a ÷ b – 3b = 5 + -5 + -12

Add from left to proper beginning with 5 and -5

a + 4a ÷ b – 3b = 0 + -12

Add 0 and -12

a + 4a ÷ b – 3b = -12

## A few examples displaying how one can consider algebraic expressions with exponents

Instance #4

Consider x3 + y2 for x = 2 and y = 2

x3 + y2 = (2)3 + (2)2

Consider the exponents

x3 + y2 = 8 + 4

Add 8 and 4

x3 + y2 = 12

Instance #5

Consider 3x2 – 4x + 2 for x = 4

3x2 – 4x + 2 = 3(4)2 – 4(4) + 2

First, consider the exponent

3×2 – 4x + 2 = 3(16) – 4(4) + 2

Carry out the multiplications by multiplying 3 and 16 and in addition 4 and 4.

3×2 – 4x + 2 = 48 – 16 + 2

Add or subtract from left to proper beginning with 48 and 16

3×2 – 4x + 2 = 32 + 2

Add 32 and a couple of

3×2 – 4x + 2 = 34

## Evaluating algebraic expressions with actual life examples

Instance #6

The algebraic expression 16t2 fashions the space in toes that an object falls throughout t seconds after being dropped from a sure distance. Discover the space an object falls after 10 seconds.

You simply want to guage 16t2 for t = 10

16t2 = 16 × t × t

16t2 = 16 × 10 × 10

Multiply from left to proper beginning with 16 and 10

16t2 = 160 × 10

Multiply 160 and 10

16t2 = 1600

The space the item fell is 1600 toes

Instance #7

Richard owns x vehicles and y vehicles. James owns 4 much less vehicles than Richard, however twice as many vehicles. Write an algebraic expression displaying the variety of autos James owns. If Richard owns 6 vehicles and a couple of vehicles, what number of car does James personal?

James owns 4 much less vehicles than Richard or x – 4

James owns twice as many vehicles as Richard or 2y

The variety of autos James owns is x – 4 + 2y

To learn the way many autos James owns, we have to consider the algebraic expression x – 4 + 2y for x = 6 and y = 2.

x – 4 + 2y = 6 – 4 + 2 × 2

First, multiply 2 and a couple of

x – 4 + 2y = 6 – 4 + 4

Add or subtract from left to proper beginning with 6 and 4

x – 4 + 2y = 2 + 4

At this level, you’ll be able to say that James owns 2 vehicles and 4 vehicles. However you might be on the lookout for the variety of autos he owns.

So, add 2 and 4

x – 4 + 2y = 6

The variety of autos James owns is 6

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