Simplify:
(i) (x−y)(x+y)(x2+y2)(x4+y4) (ii) (2x−1)(2x+1)(4x2+1)(16x4+1)
(iii) (7m−8n)2+(7m+8n)2 (iv) (2.5p−1.5q)2−(1.5p−2.5q)2
(v) (m2−n2m)2+2m3n2
(i) (x−y)(x+y)(x2+y2)(x4+y4)=(x2−y2)(x2+y2)(x4+y4)=[(x2)2−(y2)2](x4+y4)=(x4−y4)(x4+y4)=(x4)2−(y4)2=x8−y8(ii) (2x−1)(2x+1)(4x2+1)(16x4+1)=[(2x)2−(1)2](4x2+1)(16x4+1)=(4x2−1)(4x2+1)(16x4+1)=[(4x2)2−(1)2](16x4+1)=(16x4−1)(16x4+1)=(16x4)2−(1)2=256x8−1(iii) (7m−8n)2+(7m+8n)2=(7m)2+(8n)2−2×7m×8n+(7m)2+(8n)2+2×7m×8n=49m2+64n2−112mn+49m2+64n2+112mn=98m2+128n2(iv) (2.5p−1.5q)2−(1.5p−2.5q)2=(2.5p)2+(1.5q)2−2×2.5p×1.5q−[(1.5p)2+(2.5q)2−2×1.5p×2.5q]=(6.25p2+2.25q2−7.5pq)−(2.25p2+6.25q2−7.5pq)=6.25p2+2.25q2−7.5pq−2.25p2−6.25q2+7.5pq=6.25p2−2.25p2+2.25q2−6.25q2=4.00p2−4.00q2=4p2−4q2=4(p2−q2)(v) (m2−n2m)2+2m3n2=(m2)2+(n2m)2−2×m2×n2m+2m3n2=m4+n4m2−2m3n2+2m3n2=m4+n4m2=m4+m2n4