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Answer :
Sure! Let's solve this step-by-step.
We need to find the sum of the polynomials:
[tex]\[ (7x^3 - 4x^2) + (2x^3 - 4x^2) \][/tex]
### Step 1: Identify Like Terms
First, let's identify the like terms in the given polynomials. Like terms have the same variables raised to the same power.
- The terms with [tex]\( x^3 \)[/tex] are [tex]\( 7x^3 \)[/tex] and [tex]\( 2x^3 \)[/tex].
- The terms with [tex]\( x^2 \)[/tex] are [tex]\( -4x^2 \)[/tex] and [tex]\( -4x^2 \)[/tex].
### Step 2: Combine Like Terms
Now, we combine the like terms by adding their coefficients.
- Combine the [tex]\( x^3 \)[/tex] terms:
[tex]\[ 7x^3 + 2x^3 = 9x^3 \][/tex]
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[ -4x^2 + (-4x^2) = -8x^2 \][/tex]
### Step 3: Write the Result
After combining the like terms, we put them together to form the resulting polynomial:
[tex]\[ 9x^3 - 8x^2 \][/tex]
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
We need to find the sum of the polynomials:
[tex]\[ (7x^3 - 4x^2) + (2x^3 - 4x^2) \][/tex]
### Step 1: Identify Like Terms
First, let's identify the like terms in the given polynomials. Like terms have the same variables raised to the same power.
- The terms with [tex]\( x^3 \)[/tex] are [tex]\( 7x^3 \)[/tex] and [tex]\( 2x^3 \)[/tex].
- The terms with [tex]\( x^2 \)[/tex] are [tex]\( -4x^2 \)[/tex] and [tex]\( -4x^2 \)[/tex].
### Step 2: Combine Like Terms
Now, we combine the like terms by adding their coefficients.
- Combine the [tex]\( x^3 \)[/tex] terms:
[tex]\[ 7x^3 + 2x^3 = 9x^3 \][/tex]
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[ -4x^2 + (-4x^2) = -8x^2 \][/tex]
### Step 3: Write the Result
After combining the like terms, we put them together to form the resulting polynomial:
[tex]\[ 9x^3 - 8x^2 \][/tex]
So, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
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