Final answer:
To simplify algebraic expressions by combining like terms, you need to combine the coefficients of the like terms. In each expression, we combined the coefficients of the like terms to simplify the expression. We also showed all the steps in the process.
Step-by-step explanation:
To simplify each algebraic expression by combining like terms, we need to combine the coefficients of the like terms. Let's go through each expression one by one.
For the first expression, 7x^2 - 5x + 10x - 8x^2, we combine the coefficients of the x^2 terms (7 and -8) to get a combined coefficient of -1x^2. Then, we combine the coefficients of the x terms (-5 and 10) to get a combined coefficient of 5x. So, the simplified expression is:
-x^2 + 5x
For the second expression, -6a^3 + 5a^3 + 2a^2 - a^2, the coefficients of the a^3 terms (-6 and 5) cancel out, giving us a combined coefficient of -1a^3. The coefficients of the a^2 terms (2 and -1) combine to give a combined coefficient of 1a^2. So, the simplified expression is:
-a^3 + a^2
For the third expression, -4(x + 5) - 5(x - 1), we distribute the -4 and -5 to the terms inside the parentheses and combine like terms. After simplifying, we get:
-4x - 20 - 5x + 5 = -9x - 15
For the fourth expression, -a - 6a + 5a + 5b + 5, we combine the coefficients of the like terms to get:
-a - 6a + 5a + 5b + 5 = -2a + 5a + 5b + 5 = 3a + 5b + 5
Finally, for the fifth expression, 18x^4 - 3x - 2x^3 + x^2 - 10 + 6, we combine the coefficients of the x^4, x^3, x^2, x, and constant terms to get:
18x^4 - 2x^3 + x^2 - 3x - 4