help me with some math homework?

1: (x + 8)(x - 8)


2: (x + 2)2


3: (5x - 3)2


4: 4(x - 6)( x + 6)


5: (6x - 1)2


6: 6b2c2(c - 3d2)


7: 4x3(x + 10)


8: (x - 3)2


9: (x - 11)(x + 11)


10: (x + 4)2


11: (x - 11)2


12: (7x - 8)(7x + 8)


13: (4x + 5) (4x - 5)


14: (7x + 10) (7x - 10)


15: (3x + 8)2


16: 6(x - 5)2


17: 7(x + 3)(x - 3)


18:
2r2 - 162 = 0
2(r^2 - 81) = 0
2(r+9)(r-9) = 0
r = -9, 9


19:
3x3 - 3x = 0
3x(x^2 - 1) = 0
3x(x+1)(x-1) = 0
x = -1, 1


20: 81x2 + 180x + 100 = 0
(9x + 10)(9x + 10) = 0
x = -10/9

1)(x+8)(x-8)
2)(x+2)2
3)(x-5)2
4)4(x-6)(x+6)
5)(6x-1)2
6)6bc2-18bcd
7)4x3(x+10)
8)(x-3)2
9)(x-11)(x+11)
10)(x+4)2
11)(x-11)2
12)(7x-8)(7x+8)
13)(4x+5)(4x-5)
14)(7x+10)(7x-10)
15)(3x+8)2
16)6(x-5)2
17)7(x+3)(x-3)
18)r=9,-9
19) x= -1 0 1
20) x= -10/9

1)(x+8)(x-8)
2)(x+2)^2
3)(5x-3)^2
4)4(x+12)(x-12)
5)(6x-1)^2
6)6b^2c^2(c-3d^2)
7)4x^3(x+10)
8)(x-3)^2
9)(x+11)(x-11)
10)(x+4)^2
11)(x-11)^2
12)(7x+8)(7x-8)
13)(4x+5)(4x-5)
14)(7x+10)(7x-10)
15)(3x+8)^2
16)6(x-5)^2
17)7(x+3)(x-3)
18)-9 ,+9
19)-1 ,0, +1
20)-10/9

a^2 - b^2 = (a + b)(a - b)

1)
x^2 - 64
= (x + 8)(x - 8)

2)
x^2 + 4x + 4
= (x + 2)(x + 2)
= (x + 2)^2

3)
25x^2 - 30x + 9
= (5x - 3)(5x - 3)
= (5x - 3)^2

4)
4x^2 - 144
= 4(x^2 - 36)
= 4(x + 6)(x - 6)

5)
36x^2 - 12x + 1
= (6x - 1)(6x - 1)
= (6x - 1)^2

6)
6b^2c^3 - 18b^2c^2d^2
= 6(b^2c^3 - 3b^2c^2d^2)
= 6b^2c^2(c - 3d^2)

7)
4x^4 + 40x^3
= 4(x^4 + 10x^3)
= 4x^3(x + 10)

8)
x^2 - 6x + 9
= (x - 3)(x - 3)
= (x - 3)^2

9)
x^2 - 121
= (x + 11)(x - 11)

10)
x^2 + 8x + 16
= (x + 4)(x + 4)
= (x + 4)^2

11)
x^2 - 22x + 121
= (x - 11)(x - 11)
= (x - 11)^2

12)
49x^2 - 64
= (7x + 8)(7x - 8)

13)
16x^2 - 25
= (4x + 5)(4x - 5)

14)
49x^2 - 100
= (7x + 10)(7x - 10)

15)
9x^2 + 48x + 64
= (3x + 8)(3x + 8)
= (3x + 8)^2

16)
6x^2 - 60x + 150
= 6(x^2 - 10x + 25)
= 6(x - 5)(x - 5)
= 6(x - 5)^2

17)
7x^2 - 63
= 7(x^2 - 9)
= 7(x + 3)(x - 3)

= = = = = = = =

18)
2r^2 - 162 = 0
(2r^2 - 162)/2 = 0/2
r^2 - 81 = 0
(r + 9)(r - 9) = 0

r + 9 = 0
r = -9

r - 9 = 0
r = 9

∴ r = ±9

= = = = = = = =

19)
3x^3 - 3x = 0
(3x^3 - 3x)/3 = 0/3
x^3 - x = 0
x(x^2 - 1) = 0
x(x + 1)(x - 1) = 0

x = 0

x + 1 = 0
x = -1

x - 1 = 0
x = 1

∴ x = 0 , ±1

= = = = = = = =

20)
81x^2 + 180x + 100 = 0
(9x + 10)(9x + 10) = 0

9x + 10 = 0
9x = -10
x = -10/9

∴ x = -10/9

3: 25x2 - 30x + 9
25 times 9 is 225
find two numbers whose product is 225 and whose sum is -30.
-15,-15
25x^2-30x+9
=25x^2-15x-15x+9
5x(5x-3)-3(5x-3)
(5x-3)(5x-3)
(5x-3)^2

16: 6x2 - 60x + 150
product 900
sum -60
the numbers are -30,-30
6x^2-30x-30x+150
6x(x-5)-30(x-5)
(x-5)(6x-30)
(x-5)6(x-5)
6(x-5)(x-5)
6(x-5)^2

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He still doesn't know how to do the math now, since he was given the answers, and now he'll have a false grade on his homework, which will hide the fact he still doesn't know how to do it.

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Lousy people make lousy public school teachers....

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