Final answer:
To increase the first algebraic expression by the second, add the like terms of both expressions to obtain the combined expression: 4x^4 + 5x^3 + 5x^2 - 3x + 1.
Step-by-step explanation:
The question involves algebraic expression manipulation, specifically the addition of two algebraic expressions. The expressions given are:
1st Expression: 5x^3 + 7x^2 + 3x - 3
2nd Expression: 4x^4 - 2x^2 - 6x + 4
Increasing the first expression by the second means adding the respective like terms of both expressions:
- For the x^4 term, we only have it in the second expression, so it remains as it is: 4x^4.
- For the x^3 term, we only have it in the first expression, so it remains as it is: 5x^3.
- For the x^2 term, we combine 7x^2 from the first expression with -2x^2 from the second to get 5x^2.
- For the x term, we combine 3x from the first expression with -6x from the second to get -3x.
- For the constant term, we combine -3 from the first expression with +4 from the second to get +1.
So, the resultant expression after increasing the first expression by the second is:
4x^4 + 5x^3 + 5x^2 - 3x + 1
This combined expression is the result of adding the two given expressions, term by term.