Answer & Step-by-step explanation:
Let's start with the first problem.
1.) 9a⁴b⁴ - 27a³b³
Now, we have to find a number or a term that can be divisible by both terms in the expression. 9 and 27 have a common factor of 9. a⁴b⁴ and a³b³ have a common factor of a³b³. So, let's use this information to find our answer.
The GCF of the expression is 9a³b³
Now, let's do the second problem.
2.) x² - 36
For this problem, we have to factor out the expression. Since this a perfect square binomial, we can just square the terms and that will give us our answer.
The factored form of this expression is (x + 6)(x - 6)
Lastly, let's do the third problem.
3.) x² + 7x + 10
For this problem, we are going to have to factor again. First, we can break down the middle term so we can factor the expression.
x² + 2x + 5x + 10
Now, we pair the first two terms together and the last two term together.
(x² + 2x) + (5x + 10)
Now, we factor each parentheses by finding the common factor between them.
x(x + 2) + 5(x + 2)
Since, our terms are the same in each parentheses, then that means we have factored correctly.
The factored form of this expression is (x + 5)(x + 2)