maths

1.
(-5y2)2 x (-25y3) / (125y4)

= (25y4) x (-25y3) / (125y4)

= -5y4+3-4

= -5y3


2.
(2ab)3 x (2ab3) x (-b)2

= 8a3b3 x 2ab3 x b2

= 16a3+1b3+3+2

= 16a4b8


3.
(s2t)4 x (t/2s)3 / (2s)2

= (s8t4) x (t3/8s3) / (4s2)

= (1/32)s8-3-2t4+3

= s3t7/32


4.
5 x 25a x 625b

= (5)1 x (52)a x (54)b

= 51 x 52a x 54b

= 51+2a+4b


5.
210 x 2505

= 210 x (2 x 53)5

= 210 x 25 x 515

= 215 x 515

= 1015

(or 1000000000000000)


6.
(a + b + c)(a + b - c)

= [(a + b) + c][(a + b) - c]

= (a + b)2 - c2

= a2 + b2 - c2 + 2ab


7.
Let u = y + z + a

(x + y + z + a)2 - (x - y - z - a)2

= (x + u)2 - (x - u)2

= x2 - u2

= x2 - (y + z + a)2

= x2 - (y2 + z2 + a2 + 2yz + 2za + 2ya)

= x2 - y2 - z2 - a2 - 2yz - 2za - 2ya


8.
(x + y)2 - 2(x2 - y2) + (x - y)2

= x2 + 2xy + y2 - 2x2 + 2y2 + x2 - 2xy + y2

= 4y2


9.
(2xz - x2) / (3xy - 6yz)

= -x(x - 2z) / 3y(x - 2z)

= -x/3y
=