中三數學題一問=]..plz

1.
Let y = k + 1
(k+1)^2 -(k+1)-56
= y^2 - y - 56
= (y - 8)(x + 7)
= (k + 1 - 8)(k + 1 + 7)
= (k - 7)(k + 8)

2.
(2x - 3)^2 + 10x - 15
= 4x^2 - 12x + 9 + 10x - 15
= 4x^2 - 2x - 6
= 2(2x^2 - x - 3)
= 2(2x - 3)(x + 1)

3.
Let a = 3x - 2, b = 2(x + 1)
(3x-2)^3 -8(x+1)^3
= (3x - 2)^3 - [2(x + 1)]^3
= a^3 - b^3
= (a - b)(a^2 + ab + b^2)
= [(3x - 2) - 2(x + 1)][(3x - 2)^2 + (3x - 2) * 2(x + 1) + 4(x + 1)^2]
= [x - 4][9x^2 - 12x + 4 + 2(3x^2 + x - 2) + 4(x^2 + 2x + 1)]
= (x - 4)(19x^2 - 2x + 4)

4. Let x = a + b, y = a - b
(a + b)^3 + (a - b)^3
= x^3 + y^3
= (x + y)(x^2 - xy + y^2)
= (a + b + a - b)[(a + b)^2 - (a + b)(a - b) + (a - b)^2]
= 2a [a^2 + 2ab + b^2 - (a^2 - b^2) + (a^2 - 2ab + b^2)]
= 2a(a^2 + 3b^2)

5. Let a = x + 2, b = y - 3
(x+2)^2-(x+2)(y-3)-6(y-3)^2
= a^2 - ab - 6b^2
= (a - 3b)(a + 2b)
= (x + 2 - 3(y - 3))(x + 2 + 2(y - 3))
= (x - 3y + 11)(x + 2y - 4)

6. Let a = x + 7, b = x - 6
3(x+7)^2+(x+7)(x-6)-14(x-6)^2
= 3a^2 + ab - 14b^2
= (3a + 7b)(a - 2b)
= (3(x + 7) + 7(x - 6))(x + 7 - 2(x - 6))
= (10x - 21)(-x + 19)