(−3y+1)(4y2−y−7)

2 min read Jun 17, 2024
(−3y+1)(4y2−y−7)

Multiplying Polynomials: (-3y+1)(4y^2-y-7)

This article will guide you through the process of multiplying the polynomials (-3y+1) and (4y^2-y-7).

Understanding the Process

Multiplying polynomials involves distributing each term of one polynomial to every term of the other polynomial. This is similar to the distributive property you learned for single-term multiplications.

Steps for Multiplication

  1. Distribute the first term of the first polynomial:

    • Multiply -3y by each term of the second polynomial:
      • (-3y) * (4y^2) = -12y^3
      • (-3y) * (-y) = 3y^2
      • (-3y) * (-7) = 21y
  2. Distribute the second term of the first polynomial:

    • Multiply 1 by each term of the second polynomial:
      • (1) * (4y^2) = 4y^2
      • (1) * (-y) = -y
      • (1) * (-7) = -7
  3. Combine like terms:

    • -12y^3 + 3y^2 + 21y + 4y^2 - y - 7
    • Final Result: -12y^3 + 7y^2 + 20y - 7

Conclusion

Therefore, the product of (-3y+1) and (4y^2-y-7) is -12y^3 + 7y^2 + 20y - 7.

Remember, you can always check your work by substituting a value for 'y' into both the original expression and the simplified expression. If the results are equal, your multiplication was done correctly.

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