Answer :
Alright, let's solve the expression step by step.
We start with the given expression:
[tex]\[ \left[6x^9 - 10x^6 + 2x^5 - \left(-9x^9 + 2x^6 - 6x^5\right)\right] - \left[-8x^9 - 8x^6 + x^5 + \left(-4x^9 - 5x^6 - 5x^5\right)\right] \][/tex]
### Step 1: Simplify the expressions within the parentheses
For the first part:
[tex]\[ 6x^9 - 10x^6 + 2x^5 - \left(-9x^9 + 2x^6 - 6x^5\right) \][/tex]
Distribute the negative sign in the parentheses:
[tex]\[ = 6x^9 - 10x^6 + 2x^5 + 9x^9 - 2x^6 + 6x^5 \][/tex]
Combine like terms:
[tex]\[ = (6x^9 + 9x^9) + (-10x^6 - 2x^6) + (2x^5 + 6x^5) \][/tex]
[tex]\[ = 15x^9 - 12x^6 + 8x^5 \][/tex]
For the second part:
[tex]\[ -8x^9 - 8x^6 + x^5 + \left(-4x^9 - 5x^6 - 5x^5\right) \][/tex]
Distribute the negative sign in the parentheses:
[tex]\[ = -8x^9 - 8x^6 + x^5 - 4x^9 - 5x^6 - 5x^5 \][/tex]
Combine like terms:
[tex]\[ = (-8x^9 - 4x^9) + (-8x^6 - 5x^6) + (x^5 - 5x^5) \][/tex]
[tex]\[ = -12x^9 - 13x^6 - 4x^5 \][/tex]
### Step 2: Subtract the simplified expressions
So now we have:
[tex]\[ (15x^9 - 12x^6 + 8x^5) - (-12x^9 - 13x^6 - 4x^5) \][/tex]
Distribute the negative sign:
[tex]\[ = 15x^9 - 12x^6 + 8x^5 + 12x^9 + 13x^6 + 4x^5 \][/tex]
Combine like terms:
[tex]\[ = (15x^9 + 12x^9) + (-12x^6 + 13x^6) + (8x^5 + 4x^5) \][/tex]
[tex]\[ = 27x^9 + x^6 + 12x^5 \][/tex]
Thus, the final simplified expression is:
[tex]\[ x^5(27x^4 + x + 12) \][/tex]
We start with the given expression:
[tex]\[ \left[6x^9 - 10x^6 + 2x^5 - \left(-9x^9 + 2x^6 - 6x^5\right)\right] - \left[-8x^9 - 8x^6 + x^5 + \left(-4x^9 - 5x^6 - 5x^5\right)\right] \][/tex]
### Step 1: Simplify the expressions within the parentheses
For the first part:
[tex]\[ 6x^9 - 10x^6 + 2x^5 - \left(-9x^9 + 2x^6 - 6x^5\right) \][/tex]
Distribute the negative sign in the parentheses:
[tex]\[ = 6x^9 - 10x^6 + 2x^5 + 9x^9 - 2x^6 + 6x^5 \][/tex]
Combine like terms:
[tex]\[ = (6x^9 + 9x^9) + (-10x^6 - 2x^6) + (2x^5 + 6x^5) \][/tex]
[tex]\[ = 15x^9 - 12x^6 + 8x^5 \][/tex]
For the second part:
[tex]\[ -8x^9 - 8x^6 + x^5 + \left(-4x^9 - 5x^6 - 5x^5\right) \][/tex]
Distribute the negative sign in the parentheses:
[tex]\[ = -8x^9 - 8x^6 + x^5 - 4x^9 - 5x^6 - 5x^5 \][/tex]
Combine like terms:
[tex]\[ = (-8x^9 - 4x^9) + (-8x^6 - 5x^6) + (x^5 - 5x^5) \][/tex]
[tex]\[ = -12x^9 - 13x^6 - 4x^5 \][/tex]
### Step 2: Subtract the simplified expressions
So now we have:
[tex]\[ (15x^9 - 12x^6 + 8x^5) - (-12x^9 - 13x^6 - 4x^5) \][/tex]
Distribute the negative sign:
[tex]\[ = 15x^9 - 12x^6 + 8x^5 + 12x^9 + 13x^6 + 4x^5 \][/tex]
Combine like terms:
[tex]\[ = (15x^9 + 12x^9) + (-12x^6 + 13x^6) + (8x^5 + 4x^5) \][/tex]
[tex]\[ = 27x^9 + x^6 + 12x^5 \][/tex]
Thus, the final simplified expression is:
[tex]\[ x^5(27x^4 + x + 12) \][/tex]
