Math

Binomial theorem Solutions

Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.) (4x + 5y)^6 ,n=4 a)160,000x^3y^3 b)15x^2y^4 c)240x^2y^4 d)15,625y^6 e)360x^2y^4

Find the indicated terms in the expansion of (2x² - 4x + 3) (2x – 9)(5x² + 2x + 4) (A) The degree 1 term is? (B)The degree 4 term is?

Find the indicated terms in the expansion of (4x² + x - 2)(4x² + 5x – 10) (5x² + 4x + 3) (A) The degree 5 term is? (B) The degree 1 term is?

The polynomial (x + 9)⁷ (x – 5)² (- 3x² + 7x + 2)³ has degree? The leading term will be?

Suppose the binomial expansion of (x + y)^n includes the term 3003x⁶y⁸. (A) The x⁵y⁹ term in the expansion will be? (B) The x⁴y³ term in the expansion will be?

Find the indicated terms in the expansion of (4x² + x - 2)(4x² + 5x – 10) (5x² + 4x + 3) The degree 5 term is ___ The degree 1 term is ___

Suppose the binomial expansion of (2x – 3y)^n includes the term –15120x^4y^3 The x^4y^3 term in the expansion will be ___ The x^5y^3 term in the expansion will be ___

Suppose the binomial expansion of (x - y)^n includes the term – 84x^6y^3 The x^5y^4 term in the expansion will be ___ The x^6y^8 term in the expansion will be ___

Find the coefficient of the a³y¹¹ term in the expansion of (a + y)¹⁴. In the expansion, (a + y)¹⁴ = a¹⁴ + ... +___________ a³y¹¹ + ... +y¹⁴ (Enter ONLY the coefficient)

The coefficients in the polynomial expansion of (x - y) 50 alternate in sign. Select one: O a. The statement is false because the signs of the coefficients are determined by the powers of x. O b. The statement is true because the signs of a binomial expansion always alternate. O c. The statement is true because the signs of the coefficients are determined by the powers of -y. od. The statement is false because all of the values in Pascal's triangle are positive.

Pablo randomly picks three marbles from a bag of eight marbles (four red ones, three green ones, and one yellow one). How many outcomes are there in the sample space? X outcomes How many outcomes in the event that none of the marbles he picks are red? outcomes

Use the binomial theorem to prove the following statement. n - For every integer n 20, § (-1)(); - = 6". i = 0 Let n be any integer with n > 0. Apply the binomial theorem with a = 7 and b = -1. 61 = (7 + (-1))" ) ) ( (-1)" + = 0 ) ) ]) (-17 + (2XL) -17% + ... + ( [ - | (-1)();--|(-1) n i = 0

Get homework help from verified tutors

Create account for free to start getting homework help from real tutors 24/7