Factorise fully 3*a^3*b +12*a^2*b^2 + 9*a^5*b^3

To factorise 3a³b + 12a²b² + 9a⁵b³, we need to deal with like elements together.Start with the integers. The highest common factor of 3, 12, and 9 is 3. Therefore we factor out the 3 and the expression becomes3(a³b + 4a²b² + 3a⁵b³)Next, deal with the a values. The highest common factor of a³, a² and a⁵ is a². So, we factor out a²and the expression becomes3a²(ab + 4b² + 3a³b³)Finally, we need to factorise the b values. The highest common factor of b, b² and b³ is b. So we factor out b and the expression becomes.3a²b(a + 4b + 3a³b²). Therefore, the complete factorisation of 3a³b + 12a²b² + 9a⁵b³ is 3a²b(a + 4b + 3a³b²).