Question

simplify [ 5*(25)^a+1 - 25 * (5)^2a ] / [5*(5)]^2a+3 - (25)^a+1

Answer 1

(i) x

2

(x+5)−5(x+5)+25

=x

3

+5x

2

−5x−25+25

=x

3

+5x

2

−5x

(ii) a

2

b

3

+3a

2

+5b

3

+15+5

=a

2

b

3

+3a

2

+5b

3

+20

(iii) t(t

2

−s)+s

2

(t

2

−s)

=t

3

−st+s

2

t

2

−s

3

(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) 2x

2

+xy+2xy+y

2

+x

2

−xy+2xy−2y

2

=2x

2

+x

2

+y

2

−2y

2

+xy+2xy−xy+2xy

=3x

2

+4xy−y

2

(vi) x

3

−x

2

y+xy

2

+x

2

y−xy

2

+y

3

=x

3

+y

3

+(xy

2

−xy

2

)+(x

2

y−x

2

y)

=x

3

+y

3

(vii) 2.25x

2

+6xy+4.5x−6xy−16y

2

−12y−4.5x+12y

=2.25x

2

−16y

2

(viii) a(a+b+c)+b(a+b−c)+c(a+b−c)

=a

2

+ab−ac+ab+b

2

−bc+ac+bc−c

2

=a

2

+b

2

−c

2

+(ab+ab)+(bc−bc)+(ca−ca)

=a

2

+b

2

−c

2

+2ab

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