Find the coefficients c1, c2, and c3
of the product (−9t^5+2t^3)(8t^3+11t)=c1t^8+c2t^6+c3t^4
To find the coefficients c1, c2, and c3, we need to multiply the two polynomials.
(-9t^5+2t^3)(8t^3+11t)
Let's multiply each term:
-9t^5 * 8t^3 = -72t^8
-9t^5 * 11t = -99t^6
2t^3 * 8t^3 = 16t^6
2t^3 * 11t = 22t^4
Now, let's combine the like terms:
-72t^8 + 16t^6 - 99t^6 + 22t^4
Combining like terms:
= -72t^8 + 16t^6 - 99t^6 + 22t^4
= -72t^8 + (16t^6 - 99t^6) + 22t^4
= -72t^8 - 83t^6 + 22t^4
From this, we can see that c1 = -72, c2 = -83, and c3 = 22.
To find the coefficients c1, c2, and c3 of the given product, we need to multiply the two expressions: (-9t^5 + 2t^3)(8t^3 + 11t).
Let's simplify the product step by step:
1. Multiply the first terms in each expression: (-9t^5)(8t^3) = -72t^8.
2. Multiply the first term of the first expression with the second term of the second expression: (-9t^5)(11t) = -99t^6.
3. Multiply the second term of the first expression with the first term of the second expression: (2t^3)(8t^3) = 16t^6.
4. Multiply the second terms in each expression: (2t^3)(11t) = 22t^4.
Combining these results, we have:
(-9t^5 + 2t^3)(8t^3 + 11t) = -72t^8 - 99t^6 + 16t^6 + 22t^4.
Simplifying further, we combine the like terms:
-72t^8 - 99t^6 + 16t^6 + 22t^4 = -72t^8 - 83t^6 + 22t^4.
Therefore, the coefficients c1, c2, and c3 are -72, -83, and 22 respectively.
To find the coefficients c1, c2, and c3 of the product (−9t^5+2t^3)(8t^3+11t)=c1t^8+c2t^6+c3t^4, we need to expand the product and collect like terms.
First, distribute -9t^5 and 2t^3 to each term in (8t^3+11t):
-9t^5 * 8t^3 = -72t^8
-9t^5 * 11t = -99t^6
2t^3 * 8t^3 = 16t^6
2t^3 * 11t = 22t^4
Next, combine the like terms:
-72t^8 + 16t^6 - 99t^6 + 22t^4
Simplify further:
-72t^8 + (16t^6 - 99t^6) + 22t^4
This simplifies to:
-72t^8 - 83t^6 + 22t^4
Now we can see that the coefficients are:
c1 = -72
c2 = -83
c3 = 22
Therefore, the coefficients c1, c2, and c3 are -72, -83, and 22, respectively.