Simplify these expressions.
6 * a + 4 * a* a
5a² + 3a² + 2a
how would you work it out?
6 * a + 4 * a* a
written as 6a + 4a^2 would be simplified.
5a² + 3a² + 2a
= 8a² + 2a
To simplify the expression 6 * a + 4 * a * a, you need to combine like terms. Here's how you can work it out step-by-step:
1. Identify the like terms. In this expression, the like terms are the terms that have the same variable(s) raised to the same power. In this case, both terms have 'a' raised to the power of 1 and 'a' raised to the power of 2.
2. Simplify each term separately.
- For the term 6 * a, there is no like term to combine it with, so it stays as it is.
- For the term 4 * a * a, you need to multiply the coefficients (4 and 1) and add the exponents of 'a' (1 + 1). This gives you 4a².
3. Combine the simplified terms. The simplified expression becomes:
6a + 4a²
Now let's simplify the expression 5a² + 3a² + 2a. Again, we will follow similar steps:
1. Identify the like terms. In this expression, the like terms are the terms that have the same variable(s) raised to the same power. In this case, both terms have 'a' raised to the power of 2 and the last term has 'a' raised to the power of 1.
2. Simplify each term separately.
- For the term 5a², there is no like term to combine it with, so it stays as it is.
- For the term 3a², there is no like term to combine it with, so it stays as it is.
- For the term 2a, there is no like term to combine it with, so it stays as it is.
3. Combine the simplified terms. The simplified expression becomes:
5a² + 3a² + 2a
So, the simplified expressions are:
6a + 4a² and 5a² + 3a² + 2a