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

Answer:

$a=[2q^{2}r]$

$b=[3s^{2}t]$

Step-by-step 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

$a^{3} +b^{3}=(a+b)(a^{2} -ab+b^{2})$

$[2q^{2}r]^{3} +[3s^{2}t]^{3}=([2q^{2}r]+[3s^{2}t])([2q^{2}r]^{2} -[2q^{2}r][3s^{2}t]+[3s^{2}t]^{2})$

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

Answer 2

Answer:

a= 2q^2r

b=3s^t

Step-by-step explanation: