factor the expression and explain?

Question

1) 9x^2 + 6x +1
2) 1/9x^2 - 1/4
3) 49x^2 - 14x + 1
4) 20 - 5(x-3)^2

Answer 1

1) 9x^2 + 6x +1 (the first step is to factor into 2 sets of factors)
think…wat are all the possible of 9x^2…well 9x times 1x = 9x^2…and 3x times 3x = 9x^2…but which one should I choose??? Well, the factors must also ADD up to 6x (which is the middle term in the expression). 9x PLUS 1x = 10x…this can’t be right because the middle term is 6x…BUT 3x PLUS 3x = 6x…so this must be correct!

(3x + 1) (3x + 1) = 0
3x + 1 = 0 and 3x + 1 = 0
3x = -1 and 3x = -1 (divide both sides by 3)
X = -1/3 and x = -1/3

Both of these are the same answer…so u just say that x = -1/3…I’ve done this one for u…see if u can do the rest urself…Cheers =D

Answer 2

1)9x^2+6x+1
Factor by grouping:
9x^2+3x+3x+1
3x(3x+1)+1(3x+1)
(3x+1)(3x+1)
(3x+1)^2

2)1/9x^2-1/4
Use common roots:
(1/3x-1/2)(1/3x+1/2)

3)49x^2-14x+1
Same example is #1:
49x^2-7x-7x+1
7x(7x-1)-1(7x-1)
(7x-1)(7x-1)
(7x-1)^2

4)20-5(x-3)^2
Expand the last term:
20-5((x-3)(x-3))
20-5(x^2-6x+9)
20-5x^2+30x-45
-5x^2+30x-25

Factor out a -5:
-5(x^2-6x+5)
-5(x-1)(x-5)

Answer 3

9x² + 6x + 1

9x² + 3x + 3x + 1

3x(3x + 1) + 1(3x + 1)

(3x + 1)(3x + 1)

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1 / 9x² - 1/4 =

4(9x²)(1/9x² - 4(9x²)(1/4) =

4 - 9x² =

(x - 3x)(x + 3x)

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