To factor the expression 54a⁶b²+ 9ab², you can use the fact that a common factor of 54a⁶b² and 9ab² is ab².
Thus, you can rewrite the expression as:
ab²(54a⁶ + 9)
You can then factor the expression inside the parentheses using the fact that 3 is a common factor of both 54 and 9:
ab²(3 * 18a⁶ + 3 * 3)
This can be simplified as:
ab²(6a⁶ + 9)
This expression is completely factored and cannot be further simplified. Therefore, the completely factored form of the expression is:
ab²(6a⁶ + 9)