simplify the expression

Question

7b²c⁵+5b⁵c²-3b⁵c²

Answer 1

The first step will always be to combine like terms. In this case, you can see that 5b⁵c² and 3b⁵c² share the same variables and exponents. These could then be simplified to 2b⁵c². Your remaining equation would then be 7b²c⁵ + 2b⁵c². You then look to see if there is a possibility to factor out any values that would be shared between the remaining terms. In this problem you can factor out b²c² as that is the maximum value of each exponent that can be removed from terms. This would leave you with the fully simplified expression of b²c²(7c³ + 2b³).

Answer 2

First instinct might be to factor out both b² and c2, however, the two right-most terms are like terms with different coefficients. These can be subtracted:

5b⁵c²-3b⁵c² = 2b⁵c²

Leaving: 7b²c⁵ + 2b⁵c²

And the like terms can be factored out:

b²c²(7c³+2b³)