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Are the following results correct?1. a^2 - 9 = (a-3)(a+3) 2. 4a^2 - 4a + 1 =...

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anya4one | Student, Undergraduate | Honors

Posted August 9, 2011 at 3:19 AM via web

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Are the following results correct?

1. a^2 - 9 = (a-3)(a+3)

2. 4a^2 - 4a + 1 = (2a-1)(2a-1)

3. y^2 - 16y + 64 = (y-8)(y-8)

4. 81r^2 - 36rs + 4s^2 = (9r-2s)(9r-2s)

5. x^2 + 8x + 12 = (x+6)(x+2)

6. 72 + 22x + x^2 = (x-18)(x-4)

7. x^2 - x - 6 = (x-2)(x+3)

8. x^2 - 5x - 24 = (x+8)(x-3)

9. 3x^2 + 14x + 15 = (3x-5)(x-3)

10. x^2 + 4x + 3 = (x-1)(x-3)

11.4x^2 + 7x - 2 = (4x-1)(x+2)

12.16y^2 - 9 = (4y+3)(4y-3)

2 Answers | Add Yours

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted August 9, 2011 at 4:15 AM (Answer #1)

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#s 1-5 are correct.

# 6 - 10 are not correct.  For all of them, the numbers are correct, but there are errors with + and - signs.

6.  72 + 22x + x^2 = (x-18)(x-4)  should be... (x + 18)(x + 4)

7.  x^2 - x - 6 = (x-2)(x+3)  should be... (x + 2)(x - 3)

8. x^2 - 5x - 24 = (x+8)(x-3)  should be... (x - 8)(x + 3)

9. 3x^2 + 14x + 15 = (3x-5)(x-3)  should be... (3x + 5)(x + 3)

10. x^2 + 4x + 3 = (x-1)(x-3)  should be... (x + 1)(x + 3)

Remember, you can always check your answer by using FOIL or graphing.

Top Answer

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hery | College Teacher | Honors

Posted August 10, 2011 at 4:08 PM (Answer #2)

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1. a^2 - 9 = (a-3)(a+3)

= (a*a) + (a*3) + (-3*a) + (-3*3)

= a^2 + 3a – 3a – 9

= a^2 – 9 (correct)

 

2. 4a^2 - 4a + 1 = (2a-1)(2a-1)

= (2a*2a) + (2a*(-1))+ (-1*2a) + (-1*(-1))

= 4a^2 -2a – 2a +1

= 4a^2 -4a + 1 (correct)

 

3. y^2 - 16y + 64 = (y-8)(y-8)

= (y*y) + (y*(-8)) + (-8*y) + (-8*(-8))

= y^2 – 16y + 64 (correct)

 

4. 81r^2 - 36rs + 4s^2 = (9r-2s)(9r-2s)

= (9r*9r) + (9r*(-2))+ (-2s*9r)+(-2s*(-2s))

= 81r^2 – 18r – 18r + 4s^2

= 81r^2 – 36r + 4s^2 (correct)

 

5. x^2 + 8x + 12 = (x+6)(x+2)

= (x*x) + (x*2) + (6*x) + (6*2)

= x^2 + 2x + 6x + 12

= x^2 + 8x + 12 (correct)

 

6. 72 + 22x + x^2 = (x-18)(x-4)

= (x*x) + (x*(-4)) + (-18*x) + (-18*(-4))

= x^2 – 4x – 18x + 72

= x^2 – 22x + 72

= 72 – 22x + x^2 (Incorrect)

 

7. x^2 - x - 6 = (x-2)(x+3)

= (x*x) + (x*3) + (-2*x) + (-2*3)

= x^2 + 3x – 2x – 6

= x^2 + x – 6 (incorrect)

 

8. x^2 - 5x - 24 = (x+8)(x-3)

= (x*x) + (x*(-3)) + (8*x) + (8*(-3))

= x^2 -3x + 8x – 24

= x^2 + 5x – 24 (Incorrect)

 

9. 3x^2 + 14x + 15 = (3x-5)(x-3)

= (3x*x) + (3x*(-3)) + (-5*x) + (-5*(-3))

= 3x^2 – 9x – 5 x + 15

= 3x^2 – 14x + 15 (Incorrect)

 

10.  x^2 + 4x + 3 = (x-1)(x-3)

= (x*x) + (x*(-3)) + (-1*x) + (-1*(-3))

= x^2 – 3x – x + 3

= x^2 – 4x + 3 (Incorrect)

 

11.4x^2 + 7x - 2 = (4x-1)(x+2)

= (4x*x) + (4x*2) + (-1*x) + (-1*2)

= 4x^2 + 8x – x – 2

= 4x^2 + 7x – 2 (correct)

 

12.16y^2 - 9 = (4y+3)(4y-3)

= (4y*4y) + (4y*(-3)) + (3*4y) + (3*(-3))

= 16y^2 – 12y + 12y – 9

= 16y^2 – 9  (correct)

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