SOLUTION: Factor the following sum of 2 cubes, please x^3+64y^3. Factor 4r^2+21r+5 Factor if possible 9-12b+4b^2 Factor completely 3s^2-10s+8 THANK YOU!!

Question 211198: Factor the following sum of 2 cubes, please x^3+64y^3.
Factor 4r^2+21r+5
Factor if possible 9-12b+4b^2
Factor completely 3s^2-10s+8
THANK YOU!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you going

# 1

Start with the given expression.

Rewrite as . Rewrite as .

Now factor by using the sum of cubes formula. Remember the sum of cubes formula is

Multiply

-----------------------------------
Answer:

So factors to .

In other words,

# 2

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*20 = 20
2*10 = 20
4*5 = 20
(-1)*(-20) = 20
(-2)*(-10) = 20
(-4)*(-5) = 20

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	20	1+20=21
2	10	2+10=12
4	5	4+5=9
-1	-20	-1+(-20)=-21
-2	-10	-2+(-10)=-12
-4	-5	-4+(-5)=-9

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

Answer:

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

RELATED QUESTIONS
4r^2 +21r+5 factor please (answered by jim_thompson5910)

Factor Completely : 12b^3 - 86b^2 +... (answered by Earlsdon)

Factor Difference of Cubes... (answered by Alan3354)

Factor the sum of 2 cubes completely. 125+m^3 Is this right?... (answered by AnlytcPhil,tutor_paul)

Factor 12b^3 - 58b^2 +... (answered by tutorcecilia)

Completely factor the polynomial 3x*3+12x*2+3x+12 Factor the trinomial completely... (answered by lynnlo,Alan3354)

Will someone please help me with these problems? 1) Factor: x^2-9y^2 2) Factor the... (answered by unlockmath)

Will someone please help me with these problems? 1) Factor: x^2-9y^2 2) Factor... (answered by stanbon)

factor completely 4r^2 -... (answered by belle3833)