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

Rujaxso

New member
Jul 1, 2017
11
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
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,735
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:

\(\displaystyle (x+y)^2=x^2+2xy+y^2\)

Have you seen this rule before?
 

Rujaxso

New member
Jul 1, 2017
11
Thanks Mark.
Nope I haven't, I was just going off of what I know about distributing.
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
371
And here is how you would do that distribution: $(a+ h)^2= (a+ h)(a+ h)= a(a+ h)+ h(a+ h)= a^2+ ah+ ha+ h^2= a^2+ 2ah+ h^2$.
 

Rujaxso

New member
Jul 1, 2017
11
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?
 

Rujaxso

New member
Jul 1, 2017
11
When you square a binomial, the following rule applies:

\(\displaystyle (x+y)^2=x^2+2xy+y^2\)

Have you seen this rule before?
Btw
Found this under Algebra 1 > polynomials > special products on khan academy, ...I will go over that section
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
371
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.
 

Rujaxso

New member
Jul 1, 2017
11
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.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,735
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:

\(\displaystyle (x+y)^n=x^n+b^n\)

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:

\(\displaystyle \sqrt{x^2+y^2}=x+y\)