I am stuck on simplifying four problems, I cannot figure out which steps i need to make. Can you please help me.
6x^4 - 8
2a² + a²b + ab + 1
12m²p + 35nq³
a²b - a² - 2b -2
What do you mean by "simplify?" Express in factor form?
6x^4 - 8 = 6(x^4 -4/3)
= 6[x^2 + sqrt(4/3)]{x^2 - sqrt(4/3)]
The last term in brackets fan be factored one more.
a²b - a² - 2b -2 = a^2(b-1) -2(b+1)
Those don't look any "simpler" than the original versions.
Of course, I'd be happy to help you simplify those problems!
To simplify these expressions, you generally want to combine like terms, factor, and apply any applicable rules of algebra. I'll go through each problem step by step and explain the process.
1. 6x^4 - 8:
- This expression cannot be simplified further since there are no like terms to combine and no factors to apply. So, the simplified form of this expression is 6x^4 - 8.
2. 2a² + a²b + ab + 1:
- To simplify this expression, let's look for any like terms. We have two terms with a² and two terms with ab.
- Combine the terms with a²: 2a² + a² = 3a².
- Combine the terms with ab: ab + a²b = ab(1 + a).
- So, the simplified form of this expression is 3a² + ab(1 + a) + 1, or you can also write it as 3a² + ab + a³b + 1.
3. 12m²p + 35nq³:
- This expression cannot be simplified further since there are no like terms to combine and no factors to apply. So, the simplified form of this expression is 12m²p + 35nq³.
4. a²b - a² - 2b - 2:
- To simplify this expression, let's look for any like terms. We have two terms with a² and two terms with b.
- Combine the terms with a²: a²b - a² = (b - 1)a².
- Combine the terms with b: -2b.
- So, the simplified form of this expression is (b - 1)a² - 2b - 2.
Remember, these are general steps for simplifying expressions, and the specific steps may vary depending on the specific problem.