Compute the following:(i) `[a b-b a]+[a bb a]` (ii) `[a^2+b^2b^2+c^2a^2+c^2a^2+b^2]+[2a b2b c-2a c-2a b]`(iii) `[-1 4-6 8 5 16 2 8 5]+[12 7 6 8 0 5 3 2 4]` (iv) `[cos^2xsin^2xsin^2xcos^2x]+[sin^2xcos^2xcos^2xsin^2x]`

Compute the following:(i) [[a, b],[-b, a]]+[[a, b],[b ,a]] (ii) [[a^2+b^2, b^2+c^2],[a^2+c^2,a^2+b^2]]+[[2ab,2b c],[-2a c,-2a b]] (iii) [[-1 ,4,-6],[ 8 ,5, 16],[ 2, 8, 5]]+[[12 ,7, 6],[ 8, 0, 5],[ 3 ,2, 4]] (iv) [[cos^2x,sin^2x],[sin^2x,cos^2x]]+[[sin^2x,cos^2x],[cos^2x,sin^2x]]

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

compute the following : (i) [{:(a,b),(-b,a):}]+[{:(a,b),(b,a):}] (ii) [{:(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2)):}]+[{:(2ab,2bc),(-2ac,-2ab):}] (iii)[{:(-1,4,-6),(8,5,16),(2,8,5):}]+[{:(12,7,6),(8,0,5),(3,2,4):}] (iv) [{:(cos^(2)x, sin^(2)x),(sin^(2)x,cos^(2)x):}]+[{:("sin"^(2),cos^(2)x),(cos^(2) x , sin^(2)x):}]

Add the following: i) 7a b c ,\ -5a b c ,\ 9a b c ,\ -8a b c ii)2x^2y ,\ -4x^2y ,\ 6x^2y ,\ -5x^2y

Add 4a^2b-2b^2c+3c^2a+4abc-5 and a^2b+b^2-2c^2+8ab

Prove that: cos^2 2x-cos^2 6x=sin4xsin8x

Factorize each of the following expressions: (i) 4a^2+12 a b+9b^2-8a-12 b , (ii) a^2+b^2-2(a b-a c+b c)

Factorize each of the following expressions: (i) 4a^2+12 a b+9b^2-8a-12 b , (ii) a^2+b^2-2(a b-a c+b c)

Expand the following (i) (4a-b+ac)^(2) (ii) (3a-5b-c)^(2) (iii) (-x+2y-3z)^(2)

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2