Find the product of (6n + 7)(3n + 1).
Understand the Problem
The image shows examples and exercises related to multiplying polynomials and finding special products of polynomials. The task is to identify a specific question from the exercises provided in the image.
Answer
The problems are: 13. $(x^2 - 2x + 1)(x-3)$ 14. $(y^2 + 5y + 4)(3y + 2)$ 15. $(x-4)(x+2)$ 16. $(5b^2 - b - 7)(b+6)$ 17. $(z+8)(z-11)$ 18. $(2a-1)(a-3)$ 19. $(6n+7)(3n+1)$ 20. $(4n-5)(7n-3)$ 21. $(3x-2)(x+4)$ 22. $(x+11)^2$ 23. $(6y+1)^2$ 24. $(2x-y)^2$ 25. $(4a-3)^2$ 26. $(k+7)(k-7)$ 27. $(3s+5)(3s-5)$
Answer for screen readers
The exercises provided are: 13. $(x^2 - 2x + 1)(x-3)$ 14. $(y^2 + 5y + 4)(3y + 2)$ 15. $(x-4)(x+2)$ 16. $(5b^2 - b - 7)(b+6)$ 17. $(z+8)(z-11)$ 18. $(2a-1)(a-3)$ 19. $(6n+7)(3n+1)$ 20. $(4n-5)(7n-3)$ 21. $(3x-2)(x+4)$ 22. $(x+11)^2$ 23. $(6y+1)^2$ 24. $(2x-y)^2$ 25. $(4a-3)^2$ 26. $(k+7)(k-7)$ 27. $(3s+5)(3s-5)$
Steps to Solve
- Identify the section on multiplying polynomials
The section "8.2 Multiply Polynomials" contains exercises asking to find the product of polynomials.
- List the exercises in section 8.2
The exercises are numbered 13 through 21. They are: 13. $(x^2 - 2x + 1)(x-3)$ 14. $(y^2 + 5y + 4)(3y + 2)$ 15. $(x-4)(x+2)$ 16. $(5b^2 - b - 7)(b+6)$ 17. $(z+8)(z-11)$ 18. $(2a-1)(a-3)$ 19. $(6n+7)(3n+1)$ 20. $(4n-5)(7n-3)$ 21. $(3x-2)(x+4)$
- Identify the section on special products of polynomials
The section "8.3 Find Special Products of Polynomials" contains exercises asking to find the product of polynomials using special product rules.
- List the exercises in section 8.3
The exercises are numbered 22 through 27. They are: 22. $(x+11)^2$ 23. $(6y+1)^2$ 24. $(2x-y)^2$ 25. $(4a-3)^2$ 26. $(k+7)(k-7)$ 27. $(3s+5)(3s-5)$
The exercises provided are: 13. $(x^2 - 2x + 1)(x-3)$ 14. $(y^2 + 5y + 4)(3y + 2)$ 15. $(x-4)(x+2)$ 16. $(5b^2 - b - 7)(b+6)$ 17. $(z+8)(z-11)$ 18. $(2a-1)(a-3)$ 19. $(6n+7)(3n+1)$ 20. $(4n-5)(7n-3)$ 21. $(3x-2)(x+4)$ 22. $(x+11)^2$ 23. $(6y+1)^2$ 24. $(2x-y)^2$ 25. $(4a-3)^2$ 26. $(k+7)(k-7)$ 27. $(3s+5)(3s-5)$
More Information
The exercises cover two main topics: multiplying polynomials and finding special products of polynomials. The first set of exercises (13-21) involves general polynomial multiplication, while the second set (22-27) focuses on special product patterns such as the square of a binomial and the difference of squares.
Tips
- Forgetting to distribute correctly when multiplying polynomials.
- Making sign errors when multiplying negative terms.
- Not combining like terms after expanding the product.
- Incorrectly applying the special product formulas (e.g., $(a+b)^2 = a^2 + 2ab + b^2$).
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