Answer :

(i)


(x2 – y2) (x2 + y2) (x4 + y4)


= [(x2)2 – (y2)2] (x4 + y4)


= (x4 – y4) (x4 – y4)


= [(x4)2 – (y4)2]


= x8 – y8


(ii)


[(2x)2 – (1)2] (4x2 + 1) (16x4 + 1)


= (4x2 – 1) (4x2 + 1) (16x4 + 1) 1


= [(4x2)2 – (1)2] (16x4 + 1) 1


= (16x4 – 1) (16x4 + 1) 1


= [(16x4)2 – (1)2] 1


= 256x8 – 1


(iii)


(7m)2 + (8n)2 – 112mn + (7m)2 + (8n)2 + 112mn


= 49m2 + 64n2 + 49m2 + 64n2


= 98m2 + 64n2 + 64n2


= 98m2 + 128n2


(iv)


(2.5p)2 + (1.5q)2 – 2 (2.5p) (1.5q) – (1.5p)2 – (2.5q)2 + 2 (1.5p) (2.5q)


= 6.25p2 + 2.25q2 – 2.25p2 – 6.25q2


= 4p2 – 6.25q2 + 2.25q2


= 4p2 – 4q2


= 4 (p2 – q2)


(v)


(m2)2 – 2 (m2) (n2) (m) + (n2m)2 + 2m3n2


= m4 – 2m3n2 + (n2m)2 + 2m3n2


= m4 + n4m2 – 2m3n2 + 2m3n2


= m4 + m2n4


= m2 (m2 + n4)


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