Question

Use the identity below to complete the tasks:

a3 + b3 = (a + b)(a2 - ab + b2)

Use the identity for the sum of two cubes to factor 8q6r3 + 27s6t3.

What is a?
What is b?

Answer 1

a= 2q^2r

b=3s^t

Explanation:

Answer 2

`a=[2q^(2)r]`

`b=[3s^(2)t]`

Explanation:

we have

`8q^(6)r^(3)+27s^(6)t^(3)`

we know that

`8q^(6)r^(3)=(2^(3))(q^(2))^(3)r^(3)=[2q^(2)r]^(3)`

`27s^(6)t^(3)=(3^(3))(s^(2))^(3)t^(3)=[3s^(2)t]^(3)`

therefore

`a=[2q^(2)r]`

`b=[3s^(2)t]`

substitute

`a^(3) +b^(3)=(a+b)(a^(2) -ab+b^(2))`

`[2q^(2)r]^(3) +[3s^(2)t]^(3)=([2q^(2)r]+[3s^(2)t])([2q^(2)r]^(2) -[2q^(2)r][3s^(2)t]+[3s^(2)t]^(2))`

`[2q^(2)r]^(3) +[3s^(2)t]^(3)=([2q^(2)r]+[3s^(2)t])([4q^(4)r^(2)] -6[q^(2)r][s^(2)t]+[9s^(4)t^(2)])`