Chase wants to factor x2 + 10x + 25 by grouping; however, Paige says it is a special product and can factor a different way. Using complete sentences, explain and demonstrate how both methods will result in the same factors.

Question

anonymous · Answer

Well I'm pretty sure there is no immediate GCF

mathmale · Answer

Hint:  a^2 + 2ab + b^2 = (a+b)(a+b).  Where have you seen this before?

anonymous · Answer

I've seen it before but I forget what its for

anonymous · Answer

So I take it that we use that formula?  Which numbers are 'a' and which is 'b'?

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

$ x^2 + 10x + 25 $

ganeshie8 · Answer

$ x^2 + 2\times5x + 5^2$

ganeshie8 · Answer

compare it wid
$a^2 + 2ab + b^2$

anonymous · Answer

doesn't the facots you choose for 10x have to have a sum equal to 10x?

ganeshie8 · Answer

we will do that later.
For now we're working it using the short cut method :  'special product'

ganeshie8 · Answer

$x^2 + 2\times5x + 5^2$

compare it wid

$a^2 + 2ab + b^2$

$a = ?$
$b = ?$

anonymous · Answer

a is 2 and b is 5?

ganeshie8 · Answer

nope.
a = x, b = 5

ganeshie8 · Answer

simply plug a, b values in the formula :-

$a^2+2ab+b^2 = (a+b)(a+b)$

ganeshie8 · Answer

$x^2 + 2\times5x + 5^2  = (x+5)(x+5)$

ganeshie8 · Answer

thats how we do it using first method : 'special product method'

anonymous · Answer

now we simplify it?

ganeshie8 · Answer

We're done.

ganeshie8 · Answer

question is asking us to factor given polynomial. 
we factored the polynomial. So we're done. ok

anonymous · Answer

Ok, lemme right it down real quick :)

anonymous · Answer

next we have to factor by grouping I think

ganeshie8 · Answer

you need to do it using second method : 'Grouping method' also

ganeshie8 · Answer

yes !

ganeshie8 · Answer

$x^2 + 10x + 25 $

find two numbers such that :-
sum = 10
product = 25

anonymous · Answer

5 and 5

anonymous · Answer

5 + 5 = 10 and 5 * 5 = 25 :D

ganeshie8 · Answer

yup ! so group it

ganeshie8 · Answer

$x^2 + 10x + 25$

$x^2 + 5x + 5x + 25$

ganeshie8 · Answer

factor the GCF from first two terms
factor the GCF from last two terms

anonymous · Answer

x^2 + 5x + 5x + 25

shouldn't only 1 5 have an x?  5x + 5x = 10x^2 right?

ganeshie8 · Answer

5apples + 5apples = 10 apples

ganeshie8 · Answer

5x + 5x = 10x

anonymous · Answer

alright

anonymous · Answer

next we can regroup right?

ganeshie8 · Answer

$x^2 + 10x + 25$

$x^2 + 5x + 5x + 25$

$x(x+5) + 5(x+5)$

anonymous · Answer

then we make the answer into (x + 5)(x + 5)?

ganeshie8 · Answer

yup !

anonymous · Answer

then we done? :D

anonymous · Answer

yay we're done :D

anonymous · Answer

both answers are identical :)

ganeshie8 · Answer

yes we're done :)