Simplify (i) (x²−5)(x+5)+25 (ii) (a²+5)(b³+3)+5 (iii) (t+8²)(t²−s) (iv) (a+b)(c−d)+(a−b)(c+d)+2(ac+bd) (v) (x+y)(2x+y)+(x+2y)(x−y) (vi) (x+y)(x²−xy+y²) (vii) (1.5x−4y)(1.5x+4y+3)−4.5x+12y (viii) (a+b+c)(a+b−c)

(i) x²(x+5)−5(x+5)+25 = x³+5x²−5x−25+25 = x³+5x²−5x
(ii) a²b³+3a²+5b³+15+5 = a²b³+3a²+5b³+20
(iii) t(t²−s)+8²(t²−s) = t³−st+64t²−64s
(iv) a(c−d)+b(c−d)+a(c+d)−b(c+d)+2(ac+bd) = ac−ad+bc−bd+ac+ad−bc−bd+2ac+2bd = 4ac
(v) 2x²+xy+2xy+y²+(x²+2xy−xy−2y²) = 2x²+xy+2xy+y²+x²−xy+2xy−2y² = 3x²+4xy−y²
(vi) x³−x²y+xy²+x²y−xy²+y³ = x³+y³+(xy²−xy²)+(x²y−x²y) = x³+y³
(vii) (1.5x−4y)(1.5x+4y+3)−4.5x+12y = 2.25x²+6xy+4.5x−6xy−16y²−12y−4.5x+12y = 2.25x²−16y²
(viii) a(a+b−c)+b(a+b−c)+c(a+b−c) = a²+ab−ac+ab+b²−bc+ac+bc−c² = a²+b²−c²+2ab