maths! maths! maths!

a.
a2/64 - 9b2/4
= (a/8)2 - (3b/2)2
= [(a/8) - (3b/2)][(a/8) + (3b/2)]


b.
289 - x6y4
= (17)2 - (x3y2)
= (17 - x3y2)(17 + x3y2)


c.
3x6 - 48x4 + 192x2
= 3x2(x4 - 16x2 + 64)
= 3x2[(x2)2 - 2(x2)(8) + (8)2]
= 3x2(x2 - 8)2


d.
rx - ry + ty - tx
= r(x - y) + t(y - x)
= r(x - y) - t(x - y)
= (r - t)(x - y)


e.
(x + y)(2x - y) - 3x - 3y
= (x + y)(2x - y) - 3(x + y)
= (x + y)(2x - y - 3)


f.
(x + y)(2a - 3b) + (x + y)(2b - c)
= (x + y)[(2a - 3b) + (2b - c)]
= (x + y)(2a - b - c)


g.
27 - x3
= (3)3 - (x)3
= (x - y)(x2 + xy + y2)


h.
16m3
= 24m3