Simplifying f(a+h)=-5(a+h)^2+2(a+h)-1

  • Context: MHB 
  • Thread starter Thread starter Rujaxso
  • Start date Start date
  • Tags Tags
    Simplifying
Click For Summary

Discussion Overview

The discussion centers around the simplification of the expression f(a+h) = -5(a+h)^2 + 2(a+h) - 1, specifically focusing on the expansion of the squared term and the application of algebraic rules related to binomials. Participants explore the correct method for expanding the expression and clarify misunderstandings related to distribution and squaring binomials.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants express confusion about the origin of the term 2ah in the expansion of (a+h)^2.
  • One participant references the binomial expansion rule, stating that (x+y)^2 = x^2 + 2xy + y^2, and questions if others are familiar with this rule.
  • Another participant acknowledges their lack of familiarity with the binomial expansion and mentions relying on distribution instead.
  • A participant provides a detailed explanation of the distribution process for squaring a binomial.
  • Some participants discuss the need to view the entire quantity in parentheses as the base for the exponent rather than squaring each term individually.
  • One participant reflects on their previous misunderstanding of applying distribution to (B+C)^2, recognizing it as incorrect.
  • Another participant mentions a common mistake known as the "freshman's dream," which involves misapplying exponent rules.

Areas of Agreement / Disagreement

Participants generally agree on the correct approach to expanding binomials but express differing levels of understanding regarding the application of these rules. The discussion reveals multiple viewpoints on the methods of simplification, indicating that some participants are still grappling with the concepts.

Contextual Notes

Some participants demonstrate uncertainty about the rules of algebraic expansion and distribution, indicating a need for further clarification on these foundational concepts.

Rujaxso
Messages
10
Reaction score
0
Not sure where the 2ah is coming from in the middle step.

f(a+h)=-5(a+h)^2+2(a+h)-1 = -5(a^2 + 2ah +h^2) +2a +2h -1 = -5a^2 - 10ah -5h^2 +2a +2h -1

Please enlighten me
 
Physics news on Phys.org
Rujaxso said:
Not sure where the 2ah is coming from in the middle step.

f(a+h)=-5(a+h)^2+2(a+h)-1 = -5(a^2 + 2ah +h^2) +2a +2h -1 = -5a^2 - 10ah -5h^2 +2a +2h -1

Please enlighten me

When you square a binomial, the following rule applies:

$$(x+y)^2=x^2+2xy+y^2$$

Have you seen this rule before?
 
Thanks Mark.
Nope I haven't, I was just going off of what I know about distributing.
 
And here is how you would do that distribution: $(a+ h)^2= (a+ h)(a+ h)= a(a+ h)+ h(a+ h)= a^2+ ah+ ha+ h^2= a^2+ 2ah+ h^2$.
 
Okay so instead of squaring each term I need to think about the quantity as a whole in the parenthesis as being a base for the exponent?
 
MarkFL said:
When you square a binomial, the following rule applies:

$$(x+y)^2=x^2+2xy+y^2$$

Have you seen this rule before?

Btw
Found this under Algebra 1 > polynomials > special products on khan academy, ...I will go over that section
 
Rujaxso said:
Okay so instead of squaring each term I need to think about the quantity as a whole in the parenthesis as being a base for the exponent?
Yes, that's what the parentheses mean. $( )^2$ means you square whatever is in the parentheses. $( )^3$ means you cube what ever is in the parentheses. $\sin( )$ means you take the sine of whatever is in the parentheses. In general $f( )$ means you apply the function f to whatever is in the parentheses.
 
I guess I wanted to apply A(B+C) = AB + AC to (B+C)^2 and make B^2 + C^2 which is incorrect I see.
 
Rujaxso said:
I guess I wanted to apply A(B+C) = AB + AC to (B+C)^2 and make B^2 + C^2 which is incorrect I see.

Thinking that:

$$(x+y)^n=x^n+b^n$$

is a mistake so commonly made by students, it's been given a name...the "freshman's dream." :)

I have also seen a lot of students make a related mistake, and that is to state:

$$\sqrt{x^2+y^2}=x+y$$
 

Similar threads

Undergrad Multivariable Differentiation .... McInerney Definition 3.1.1 ....
  • · Replies 22 ·
Replies
22
Views
4K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
The volume of a "spherical cap" using triple integrals
  • · Replies 9 ·
Replies
9
Views
2K
MHB Solving Function Expressions h(x): (x+a)2 +b & h-1 Range
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
MHB Limit x to o: $\lim_{h\to 0}=-\frac{1}{5}$
  • · Replies 2 ·
Replies
2
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
2K
MHB Derivative of f(x), g(x) and h(x) from Calculus Problem A.1: Solve Urgent"
  • · Replies 5 ·
Replies
5
Views
1K
High School Applying L'Hospital's rule to Integration as the limit of a sum
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Recovering some math notions: Variations
  • · Replies 4 ·
Replies
4
Views
1K