Answer:
1) 5y + 5z
2) 10x⁴ - 10x³ + 2x² + 18x - 11
Step-by-step explanation:
Given the subtraction of the following polynomial expressions:
<h2>(1) -3x - 4y + 11z from -9y + 6z - 3x</h2>In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the <em>subtrahend</em> by alphabetical order.
-3x - 4y + 11z
-3x - 9y + 6z ⇒ This is the <u><em>subtrahend</em></u>.
Now, we can finally perform the subtraction on both trinomials:
In the <em>subtrahend</em>, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.
The difference is: 5y + 5z.
<h2>(2) 3x⁴- 4x³ + 7x - 2 from 9 - 7x⁴ + 6x³- 2x² - 11x</h2>
Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.
3x⁴- 4x³ + 7x - 2 ⇒ Already in descending order (degree).
9 - 7x⁴ + 6x³- 2x² - 11x ⇒ -7x⁴ + 6x³- 2x² - 11x + 9
In subtracting polynomials, we can only subtract <u>like terms</u>, which are terms that have the same variables and exponents.
In the <u><em>minuend</em></u><em>, </em>I added the "0x²" to make it less-confusing for us to perform the subtraction operations.
The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x ⇒ their coefficients turn into positive when performing subtraction.
Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.