(4y2%E2%88%92y%E2%88%927).jpeg "(−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
-
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
- Multiply -3y by each term of the second polynomial:
-
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
- Multiply 1 by each term of the second polynomial:
-
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.