Answer :
Let's subtract and simplify the given polynomials step-by-step:
We have the first polynomial:
[tex]\( 8x^6 + 8x^5 - 10x^4 - 7x^2 \)[/tex]
And the second polynomial:
[tex]\( 10x^6 - 2x^5 + 2x^3 + 5x^2 \)[/tex]
To subtract the second polynomial from the first, we need to subtract the coefficients of like terms.
1. Subtract the coefficients of [tex]\(x^6\)[/tex]:
[tex]\((8) - (10) = -2\)[/tex]
2. Subtract the coefficients of [tex]\(x^5\)[/tex]:
[tex]\((8) - (-2) = 10\)[/tex]
3. Subtract the coefficients of [tex]\(x^4\)[/tex]:
[tex]\((-10) - (0) = -10\)[/tex]
4. Subtract the coefficients of [tex]\(x^3\)[/tex]:
[tex]\((0) - (2) = -2\)[/tex]
5. Subtract the coefficients of [tex]\(x^2\)[/tex]:
[tex]\((-7) - (5) = -12\)[/tex]
6. Combine the results to form the simplified polynomial:
[tex]\(-2x^6 + 10x^5 - 10x^4 - 2x^3 - 12x^2\)[/tex]
So, the polynomial you get after subtraction and simplification is:
[tex]\(-2x^6 + 10x^5 - 10x^4 - 2x^3 - 12x^2\)[/tex]
We have the first polynomial:
[tex]\( 8x^6 + 8x^5 - 10x^4 - 7x^2 \)[/tex]
And the second polynomial:
[tex]\( 10x^6 - 2x^5 + 2x^3 + 5x^2 \)[/tex]
To subtract the second polynomial from the first, we need to subtract the coefficients of like terms.
1. Subtract the coefficients of [tex]\(x^6\)[/tex]:
[tex]\((8) - (10) = -2\)[/tex]
2. Subtract the coefficients of [tex]\(x^5\)[/tex]:
[tex]\((8) - (-2) = 10\)[/tex]
3. Subtract the coefficients of [tex]\(x^4\)[/tex]:
[tex]\((-10) - (0) = -10\)[/tex]
4. Subtract the coefficients of [tex]\(x^3\)[/tex]:
[tex]\((0) - (2) = -2\)[/tex]
5. Subtract the coefficients of [tex]\(x^2\)[/tex]:
[tex]\((-7) - (5) = -12\)[/tex]
6. Combine the results to form the simplified polynomial:
[tex]\(-2x^6 + 10x^5 - 10x^4 - 2x^3 - 12x^2\)[/tex]
So, the polynomial you get after subtraction and simplification is:
[tex]\(-2x^6 + 10x^5 - 10x^4 - 2x^3 - 12x^2\)[/tex]
