Answer :
To simplify the expression [tex]\((5x^2 - 6x + 1)(4x + 9)\)[/tex], we need to distribute each term in the first polynomial by each term in the second polynomial.
Here's a step-by-step breakdown:
1. Multiply each term in [tex]\((5x^2 - 6x + 1)\)[/tex] by [tex]\(4x\)[/tex]:
- [tex]\(5x^2 \times 4x = 20x^3\)[/tex]
- [tex]\(-6x \times 4x = -24x^2\)[/tex]
- [tex]\(1 \times 4x = 4x\)[/tex]
2. Multiply each term in [tex]\((5x^2 - 6x + 1)\)[/tex] by [tex]\(9\)[/tex]:
- [tex]\(5x^2 \times 9 = 45x^2\)[/tex]
- [tex]\(-6x \times 9 = -54x\)[/tex]
- [tex]\(1 \times 9 = 9\)[/tex]
3. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(20x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 - 24x^2 = 21x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-54x + 4x = -50x\)[/tex]
- The constant term: [tex]\(9\)[/tex]
Putting it all together, we have:
[tex]\[ 20x^3 + 21x^2 - 50x + 9 \][/tex]
Thus, the simplified form of the expression is:
[tex]\[ \boxed{20x^3 + 21x^2 - 50x + 9} \][/tex]
So, the correct answer is option C: [tex]\(20x^3 + 21x^2 - 50x + 9\)[/tex].
Here's a step-by-step breakdown:
1. Multiply each term in [tex]\((5x^2 - 6x + 1)\)[/tex] by [tex]\(4x\)[/tex]:
- [tex]\(5x^2 \times 4x = 20x^3\)[/tex]
- [tex]\(-6x \times 4x = -24x^2\)[/tex]
- [tex]\(1 \times 4x = 4x\)[/tex]
2. Multiply each term in [tex]\((5x^2 - 6x + 1)\)[/tex] by [tex]\(9\)[/tex]:
- [tex]\(5x^2 \times 9 = 45x^2\)[/tex]
- [tex]\(-6x \times 9 = -54x\)[/tex]
- [tex]\(1 \times 9 = 9\)[/tex]
3. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(20x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 - 24x^2 = 21x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-54x + 4x = -50x\)[/tex]
- The constant term: [tex]\(9\)[/tex]
Putting it all together, we have:
[tex]\[ 20x^3 + 21x^2 - 50x + 9 \][/tex]
Thus, the simplified form of the expression is:
[tex]\[ \boxed{20x^3 + 21x^2 - 50x + 9} \][/tex]
So, the correct answer is option C: [tex]\(20x^3 + 21x^2 - 50x + 9\)[/tex].
