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

Below ^ denotes power.

8q^6r^3=(2q^2r)^3 denote as a^3 and find a=2q^2r

27s^6t^3=(3s^2t)^3 denote as b^3 and find b=3s^2t

Now 8q^6r^3+27s^6t^3=a^3+b^3

= (a+b)(a^2-ab+b^2) | substitute back

=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2).

Notice (2q^2r)^2=4q^4r^2 (3s^2t)^2=9s^4t^2.

Hence 8q^6r^3+27s^6t^3=(2rq^2+3ts^2)(4r^2q^4-6rts^2t^2+9t^2s^4),

a=2q^2r and b=3s^2t.