$a^{2} - 81 = (a - 9)(a + 9)$

$x^{2} - 10x - x = $

$25x^{2} + 30x + 9x^{2} = (5x)^{2} + (4x)^{2} + (3x)^{2}$

$7 - x^{2} + y^{2} - 7 = $

$3x^{2} - 6x - 24 = 3(x^{2} - 2x - 8) = 3(x - 4)(x + 2)$

$a^{3} - a^{2} - 2a = a(a^{2} - a - 2) = a(a - 2)(a + 1)$

$5d - 15 = 5(d - 3)$

$3b^{2} - 12b + 12 = 3(b^{2} - 4b + 4) = 3(b - 2)^{2}$

$(x + 4)^{2} = (x + 4)(x + 4) = x^{2} + 8x + 16$

$(6x + 3)^{2} = (6x + 3)(6x + 3) = 36x^{2} + 36x + 9$

$(4 + 7)^{2} = (4 + 7)(4 + 7) = (7)(7) = 49$

$x^{2} + 14x + 49 = (x + 7)(x + 7) = (x + 7)^{2}$

$x^{2} + 14x + 40 = (x + 10)(x + 4)$

$m^{2} + m + 2 = (m(m + 1)) + 2$

-6 - y + y^{2} = -6 - y(1 - y)$