multiply vertically
(x^2-6x+2)(7x^2+9x+9)
To multiply vertically, we need to align the terms and then multiply each term in the first polynomial by each term in the second polynomial. Let's split the process into two steps:
Step 1: Multiply each term in the first polynomial by the entire second polynomial:
(x^2 - 6x + 2) * 7x^2 = 7x^4 - 42x^3 + 14x^2
(x^2 - 6x + 2) * 9x = 9x^3 - 54x^2 + 18x
(x^2 - 6x + 2) * 9 = 9x^2 - 54x + 18
Step 2: Add the products obtained in Step 1:
7x^4 - 42x^3 + 14x^2 + 9x^3 - 54x^2 + 18x + 9x^2 - 54x + 18
Combining like terms, we have:
7x^4 + (-42 + 9)x^3 + (14 - 54 + 9)x^2 + (18 - 54)x + 18
7x^4 - 33x^3 - 31x^2 - 36x + 18
Therefore, the vertical multiplication of (x^2 - 6x + 2)(7x^2 + 9x + 9) is 7x^4 - 33x^3 - 31x^2 - 36x + 18.