Answer :
Certainly! Let's multiply the polynomials step-by-step:
We have two polynomials:
1. [tex]\( 7x^2 + 9x + 7 \)[/tex]
2. [tex]\( 9x - 4 \)[/tex]
We need to multiply these polynomials together.
Step 1: Multiply each term in the first polynomial by each term in the second polynomial.
- Multiply [tex]\( 7x^2 \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 7x^2 \times 9x = 63x^3 \][/tex]
- Multiply [tex]\( 7x^2 \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 7x^2 \times (-4) = -28x^2 \][/tex]
- Multiply [tex]\( 9x \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 9x \times 9x = 81x^2 \][/tex]
- Multiply [tex]\( 9x \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 9x \times (-4) = -36x \][/tex]
- Multiply [tex]\( 7 \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 7 \times 9x = 63x \][/tex]
- Multiply [tex]\( 7 \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 7 \times (-4) = -28 \][/tex]
Step 2: Combine all the results:
[tex]\[ 63x^3 - 28x^2 + 81x^2 - 36x + 63x - 28 \][/tex]
Step 3: Combine the like terms:
- The [tex]\( x^2 \)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2 \)[/tex]
- The [tex]\( x \)[/tex] terms: [tex]\(-36x + 63x = 27x \)[/tex]
Putting it all together, the final result of the multiplication is:
[tex]\[ 63x^3 + 53x^2 + 27x - 28 \][/tex]
So, the correct answer is B. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
We have two polynomials:
1. [tex]\( 7x^2 + 9x + 7 \)[/tex]
2. [tex]\( 9x - 4 \)[/tex]
We need to multiply these polynomials together.
Step 1: Multiply each term in the first polynomial by each term in the second polynomial.
- Multiply [tex]\( 7x^2 \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 7x^2 \times 9x = 63x^3 \][/tex]
- Multiply [tex]\( 7x^2 \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 7x^2 \times (-4) = -28x^2 \][/tex]
- Multiply [tex]\( 9x \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 9x \times 9x = 81x^2 \][/tex]
- Multiply [tex]\( 9x \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 9x \times (-4) = -36x \][/tex]
- Multiply [tex]\( 7 \)[/tex] by [tex]\( 9x \)[/tex]:
[tex]\[ 7 \times 9x = 63x \][/tex]
- Multiply [tex]\( 7 \)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 7 \times (-4) = -28 \][/tex]
Step 2: Combine all the results:
[tex]\[ 63x^3 - 28x^2 + 81x^2 - 36x + 63x - 28 \][/tex]
Step 3: Combine the like terms:
- The [tex]\( x^2 \)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2 \)[/tex]
- The [tex]\( x \)[/tex] terms: [tex]\(-36x + 63x = 27x \)[/tex]
Putting it all together, the final result of the multiplication is:
[tex]\[ 63x^3 + 53x^2 + 27x - 28 \][/tex]
So, the correct answer is B. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
