in the first, each term contains a power of a and a power of b. You need to find the highest power of a and b that divides each term. That would look like
a^2 a^2 b + a^2 b^2 b
Now factor out the a^2 b, leaving the indicated solution. Recall that
a^m a^n = a^(m+n)
Review the properties of exponents, and the distributive law.
For the second one, recall that
(z+a)(z+b) = z^2 + (a+b)z + ab
So, you want two numbers that are factors of 45, and add up to 18.
45 has factors of
1,3,5,9,15,45
Take the factors in pairs, working in from both ends, until you find the pair that adds up to 18.
Skill in factoring comes only from experience. Do lots of these. You can use sites like wolframalpha.com to check your results.
222 - Steve, Wednesday, October 22, 2014 at 12:02am
I assume you want to factor the expressions?
a^4b + a^2b^3 = a^2b(a^2+b^2)
z^2 + 18z + 45 = (z+3)(z+15)
•Math 222 - Monica, Wednesday, October 22, 2014 at 12:10am
Thank you Steve and can you please explain how you got both answers, so that I can get a better understanding. Thanks
1 answer