Multiply polynomial $6 + 8 n^{2} - 3 n$ by $- 1 + 7 n^{3} - 3 n^{2}$ .

Answer

$(6 + 8 n^{2} - 3 n) \cdot (- 1 + 7 n^{3} - 3 n^{2}) = 56 n^{5} - 45 n^{4} + 51 n^{3} - 26 n^{2} + 3 n - 6$

Explanation

Step 1: First we have to write polynomials in descending order.

P (x) Q (x) = 8 n^{2} - 3 n + 6 = 7 n^{3} - 3 n^{2} - 1

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

7 n^{3} - 3 n^{2} - 1 8 n^{2} - 3 n 6

Fill in each empty box by multiplying the intersecting terms.

7 n^{3} - 3 n^{2} - 1 8 n^{2} 56 n^{5} - 24 n^{4} - 8 n^{2} - 3 n - 21 n^{4} 9 n^{3} 3 n 6 42 n^{3} - 18 n^{2} - 6

Combine like terms:

56 n^{5} - 21 n^{4} - 24 n^{4} + 42 n^{3} + 9 n^{3} - 8 n^{2} - 18 n^{2} + 3 n - 6 = 56 n^{5} - 45 n^{4} + 51 n^{3} - 26 n^{2} + 3 n - 6

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Multiply polynomial 6+8n2−3n by −1+7n3−3n2.

(6+8n2−3n)⋅(−1+7n3−3n2)=56n5−45n4+51n3−26n2+3n−6

Multiply polynomial $6 + 8 n^{2} - 3 n$ by $- 1 + 7 n^{3} - 3 n^{2}$ .

$(6 + 8 n^{2} - 3 n) \cdot (- 1 + 7 n^{3} - 3 n^{2}) = 56 n^{5} - 45 n^{4} + 51 n^{3} - 26 n^{2} + 3 n - 6$