Question

Multiply the polynomial, (-2k²y+5y)*(4k²+k+23)2

Answer 1

To find the product of the given polynomials, we multiply each term of the first polynomial by each term of the second polynomial and then combine like terms to get -8k⁴y - 2k³y - 26k²y + 5ky + 115y.

Step-by-step explanation:

To multiply the polynomial (-2k²y+5y)(4k²+k+23), we'll use the distributive property (also known as the FOIL method in the case of binomials). This involves multiplying each term of the first polynomial by every term of the second polynomial and then combining like terms.

First, multiply -2k²y by each term of the second polynomial:

• 
  `-2k²y * 4k² = -8k⁴y`
• 
  `-2k²y * k = -2k³y`
• 
  `-2k²y * 23 = -46k²y`

Next, multiply 5y by each term of the second polynomial:

• 
  `5y * 4k² = 20k²y`
• 
  `5y * k = 5ky`
• 
  `5y * 23 = 115y`

Now, combine the like terms to achieve the final result:

• -8k⁴y + -2k³y + (-46k²y + 20k²y) + 5ky + 115y
• Which simplifies to -8k⁴y - 2k³y - 26k²y + 5ky + 115y

So the result of multiplying the given polynomials is -8k⁴y - 2k³y - 26k²y + 5ky + 115y.