Perform the following additions and/or subtractions:
$\left(8 h^4-2 h-4\right)-\left(-7 h^4+6 h+5\right)=$
$\square$
Answer (1)
Distribute the negative sign: 8 h 4 − 2 h − 4 + 7 h 4 − 6 h − 5 .
Combine like terms: ( 8 h 4 + 7 h 4 ) + ( − 2 h − 6 h ) + ( − 4 − 5 ) .
Simplify: 15 h 4 − 8 h − 9 .
The final answer is 15 h 4 − 8 h − 9 .
Explanation
Understanding the problem We are asked to simplify the expression ( 8 h 4 − 2 h − 4 ) − ( − 7 h 4 + 6 h + 5 ) . This involves distributing the negative sign and combining like terms.
Distributing the negative sign First, distribute the negative sign to each term inside the second parentheses: 8 h 4 − 2 h − 4 − ( − 7 h 4 ) − ( 6 h ) − ( 5 ) = 8 h 4 − 2 h − 4 + 7 h 4 − 6 h − 5
Combining like terms Next, combine the like terms. We have h 4 terms, h terms, and constant terms. ( 8 h 4 + 7 h 4 ) + ( − 2 h − 6 h ) + ( − 4 − 5 ) 15 h 4 − 8 h − 9
Final result Therefore, the simplified expression is 15 h 4 − 8 h − 9 .
Examples
Polynomial subtraction is used in various fields such as engineering, physics, and computer graphics. For example, in computer graphics, subtracting polynomials can help determine the difference between two curves or surfaces, which is essential for rendering and modeling objects. In physics, it can be used to find the net force acting on an object when multiple forces are described by polynomial functions.
