Distribution in Algebra: Calculating 16(1+h)^2 - 16(1)^2/h

In summary, the conversation discusses a calculus problem in which the algebra portion is causing difficulty. The solution involves simplifying an expression, taking a common factor, and considering the limit as h approaches 0. The summary provides a step-by-step explanation of the solution process.
  • #1
robertjford80
388
0

Homework Statement


This is a calc problem but it's the algebra part I'm having trouble with:

Screenshot2012-05-21at11120AM.png






The Attempt at a Solution



[16(1+h)2 - 16(1)2]/h

[16 + 32h + 16h2 - 162]/h

= 16/h + 32 + 16h - 162

this is a calc problem so h approaches zero

= 32 + 16h - 162

= 16(h + 2) - 162

I can't figure out why - 162 disappears.
 
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  • #2


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  • #3


robertjford80 said:
= 16/h + 32 + 16h - 162

this is a calc problem so h approaches zero

= 32 + 16h - 162

What happened to that 16/h?? Surely, as h -> 0 16/h is -not- equal to 0.



Try taking the 16 common out of the original expression, giving you

[tex]\frac{16((1+h)^2-1)}{h}[/tex]

Simplify this further, that should lead you to your answer.
 

1. What is distribution in algebra?

Distribution in algebra refers to the process of multiplying each term inside parentheses by a factor outside the parentheses. This is also known as the distributive property and is a fundamental rule in algebra that helps simplify equations and expressions.

2. How do you distribute in algebra?

To distribute in algebra, you need to multiply the factor outside the parentheses by each term inside the parentheses. For example, in the equation 2(a + b), the factor 2 would be distributed to both a and b, resulting in 2a + 2b.

3. What does "16(1+h)^2" mean in the equation?

The expression "16(1+h)^2" means that the factor 16 is being distributed to both 1 and h, and the exponent 2 indicates that the entire expression inside the parentheses is being squared.

4. Why is there a negative sign in front of "16(1)^2/h"?

The negative sign indicates that the term "16(1)^2/h" is being subtracted from the first term "16(1+h)^2". This is a common practice in algebra when simplifying equations.

5. How do you solve the equation "16(1+h)^2 - 16(1)^2/h"?

To solve this equation, you need to first distribute the factors outside the parentheses, resulting in 16(1+2h+h^2) - (16/h). Then, you can combine like terms and simplify further to get the final answer.

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