Question

Factorise:
a) 1 + 64x^3
b) a^3–8b^3

Answer 1

Step-by-step explanation:

We know,

(a

3

+b

3

)=a

3

+a

2

b−a

2

b−ab

2

+ab

2

+b

3

=(a

3

+a

2

b)−(a

2

b+ab

2

)+(ab

2

+b

3

)

=a

2

(a+b)−ab(a+b)+b

2

(a+b)

=(a+b)(a

2

−ab+b

2

)

Now, given, 1+64x

3

=1

3

+(4x)

3

=(1+4x)(1−4x(1)+(4x

2

))

=(1+4x)(1−4x+16x

2

)