Final answer:
The simplified form of the expression (2y-1)×(4y¹⁰+2y⁹+4y⁸+2y⁷) is 8y¹¹ + 6y⁹ - 2y⁷, which is not listed in the given options. Therefore, the correct answer is D. None of the above.
Step-by-step explanation:
To find the simplified form of the expression (2y-1)×(4y¹⁰+2y⁹+4y⁸+2y⁷), we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to multiply each term in the first polynomial by each term in the second polynomial.
Let's perform the multiplication step-by-step:
- First, multiply 2y by each term of the second polynomial:
(2y)×(4y¹⁰) = 8y¹¹
(2y)×(2y⁹) = 4y¹⁰
(2y)×(4y⁸) = 8y⁹
(2y)×(2y⁷) = 4y⁸ - Then, multiply -1 by each term of the second polynomial:
(-1)×(4y¹⁰) = -4y¹⁰
(-1)×(2y⁹) = -2y⁹
(-1)×(4y⁸) = -4y⁸
(-1)×(2y⁷) = -2y⁷
We combine like terms to get the final polynomial:
8y¹¹ + (4y¹⁰ - 4y¹⁰) + (8y⁹ - 2y⁹) + (4y⁸ - 4y⁸) - 2y⁷
Simplifying further by canceling out the terms that reduce to zero:
8y¹¹ + 0y¹⁰ + 6y⁹ + 0y⁸ - 2y⁷
The simplified form of the expression is 8y¹¹ + 6y⁹ - 2y⁷, which is not one of the options given in the question. Hence, the correct answer is D. None of the above.