Sure! Let's break down the process of adding the polynomials [tex]\( (9x^3 + 7x - 7) + (10x^2 - 8x + 5) \)[/tex] step by step.
1. Arrange the polynomials in a horizontal format, grouping like terms together:
[tex]\[
9x^3 + 7x - 7 + 10x^2 - 8x + 5
\][/tex]
2. Combine like terms:
- The [tex]\( x^3 \)[/tex] term: [tex]\( 9x^3 \)[/tex]
- The [tex]\( x^2 \)[/tex] term: [tex]\( 10x^2 \)[/tex]
- The [tex]\( x \)[/tex] terms: [tex]\( 7x - 8x \)[/tex]
- The constant terms: [tex]\( -7 + 5 \)[/tex]
3. Perform the addition for the coefficients of each like term:
- For the [tex]\( x^3 \)[/tex] term: [tex]\( 9x^3 \)[/tex]
- For the [tex]\( x^2 \)[/tex] term: [tex]\( 10x^2 \)[/tex]
- For the [tex]\( x \)[/tex] terms: [tex]\( 7x - 8x = -1x \)[/tex]
- For the constant terms: [tex]\( -7 + 5 = -2 \)[/tex]
4. Write the simplified polynomial by combining the results:
[tex]\[
9x^3 + 10x^2 - 1x - 2
\][/tex]
This simplifies to:
[tex]\[
\boxed{9x^3 + 10x^2 - x - 2}
\][/tex]
Thus, the completely simplified answer is [tex]\( 9x^3 + 10x^2 - x - 2 \)[/tex].
