Answer :
To find the expression equivalent to [tex]\((6x^8 + 7x^7 - 3x^6 + 1) - (3x^8 - 4x^7 + 7x^6 - 6)\)[/tex], let's work through the subtraction step by step:
1. Distribute the Negative Sign:
We first need to distribute the negative sign through the second polynomial expression. This means we change the signs of each term inside the second set of parentheses:
[tex]\[
-(3x^8 - 4x^7 + 7x^6 - 6) = -3x^8 + 4x^7 - 7x^6 + 6
\][/tex]
2. Combine the Expressions:
Now, we combine the first expression with the modified second expression:
[tex]\[
(6x^8 + 7x^7 - 3x^6 + 1) + (-3x^8 + 4x^7 - 7x^6 + 6)
\][/tex]
3. Combine Like Terms:
Group and simplify the like terms:
- For [tex]\(x^8\)[/tex] terms: [tex]\(6x^8 - 3x^8 = 3x^8\)[/tex]
- For [tex]\(x^7\)[/tex] terms: [tex]\(7x^7 + 4x^7 = 11x^7\)[/tex]
- For [tex]\(x^6\)[/tex] terms: [tex]\(-3x^6 - 7x^6 = -10x^6\)[/tex]
- For the constant terms: [tex]\(1 + 6 = 7\)[/tex]
4. Write the Simplified Expression:
When we combine all the simplified terms, the resulting expression is:
[tex]\[
3x^8 + 11x^7 - 10x^6 + 7
\][/tex]
Therefore, the expression equivalent to the original problem is [tex]\(3x^8 + 11x^7 - 10x^6 + 7\)[/tex]. This is the simplified expression you get when you perform the subtraction and combine like terms.
1. Distribute the Negative Sign:
We first need to distribute the negative sign through the second polynomial expression. This means we change the signs of each term inside the second set of parentheses:
[tex]\[
-(3x^8 - 4x^7 + 7x^6 - 6) = -3x^8 + 4x^7 - 7x^6 + 6
\][/tex]
2. Combine the Expressions:
Now, we combine the first expression with the modified second expression:
[tex]\[
(6x^8 + 7x^7 - 3x^6 + 1) + (-3x^8 + 4x^7 - 7x^6 + 6)
\][/tex]
3. Combine Like Terms:
Group and simplify the like terms:
- For [tex]\(x^8\)[/tex] terms: [tex]\(6x^8 - 3x^8 = 3x^8\)[/tex]
- For [tex]\(x^7\)[/tex] terms: [tex]\(7x^7 + 4x^7 = 11x^7\)[/tex]
- For [tex]\(x^6\)[/tex] terms: [tex]\(-3x^6 - 7x^6 = -10x^6\)[/tex]
- For the constant terms: [tex]\(1 + 6 = 7\)[/tex]
4. Write the Simplified Expression:
When we combine all the simplified terms, the resulting expression is:
[tex]\[
3x^8 + 11x^7 - 10x^6 + 7
\][/tex]
Therefore, the expression equivalent to the original problem is [tex]\(3x^8 + 11x^7 - 10x^6 + 7\)[/tex]. This is the simplified expression you get when you perform the subtraction and combine like terms.
