Are the following results correct?1. a^2 2. 4a^2 3. y^2 4. 81r^2 - 36rs + 4s^2 =...

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)