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Answer :
To multiply the polynomials
[tex]$$ (9x + 7)(3x^2 + 5x - 1), $$[/tex]
we can use the distributive property (also known as the FOIL method when applicable):
1. Multiply the first term of the first polynomial by each term of the second polynomial:
- [tex]$$ 9x \cdot 3x^2 = 27x^3, $$[/tex]
- [tex]$$ 9x \cdot 5x = 45x^2, $$[/tex]
- [tex]$$ 9x \cdot (-1) = -9x. $$[/tex]
2. Multiply the second term of the first polynomial by each term of the second polynomial:
- [tex]$$ 7 \cdot 3x^2 = 21x^2, $$[/tex]
- [tex]$$ 7 \cdot 5x = 35x, $$[/tex]
- [tex]$$ 7 \cdot (-1) = -7. $$[/tex]
3. Combine the results by adding like terms:
- The cubic term: [tex]$$ 27x^3, $$[/tex]
- The quadratic terms: [tex]$$ 45x^2 + 21x^2 = 66x^2, $$[/tex]
- The linear terms: [tex]$$ -9x + 35x = 26x, $$[/tex]
- The constant term: [tex]$$ -7. $$[/tex]
Thus, the final product is:
[tex]$$ 27x^3 + 66x^2 + 26x - 7. $$[/tex]
[tex]$$ (9x + 7)(3x^2 + 5x - 1), $$[/tex]
we can use the distributive property (also known as the FOIL method when applicable):
1. Multiply the first term of the first polynomial by each term of the second polynomial:
- [tex]$$ 9x \cdot 3x^2 = 27x^3, $$[/tex]
- [tex]$$ 9x \cdot 5x = 45x^2, $$[/tex]
- [tex]$$ 9x \cdot (-1) = -9x. $$[/tex]
2. Multiply the second term of the first polynomial by each term of the second polynomial:
- [tex]$$ 7 \cdot 3x^2 = 21x^2, $$[/tex]
- [tex]$$ 7 \cdot 5x = 35x, $$[/tex]
- [tex]$$ 7 \cdot (-1) = -7. $$[/tex]
3. Combine the results by adding like terms:
- The cubic term: [tex]$$ 27x^3, $$[/tex]
- The quadratic terms: [tex]$$ 45x^2 + 21x^2 = 66x^2, $$[/tex]
- The linear terms: [tex]$$ -9x + 35x = 26x, $$[/tex]
- The constant term: [tex]$$ -7. $$[/tex]
Thus, the final product is:
[tex]$$ 27x^3 + 66x^2 + 26x - 7. $$[/tex]
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