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

[Rujaxso]

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]

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?

 

[Rujaxso]

Thanks Mark.
Nope I haven't, I was just going off of what I know about distributing.

 

[HOI]

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]

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]

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

 

[HOI]

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]

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]

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:

$$\sqrt{x^2+y^2}=x+y$$

 

[Rujaxso]

https://en.wikipedia.org/wiki/Freshman's_dream

****(french) its official